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Systems of Equations and Inequalities - Unit Bundle (Updated October 2016)

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ALGEBRA 1
Unit
5
Created by: ALL THINGS ALGEBRA®
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© 2012-2015 Gina Wilson (All Things Algebra)
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Unit 5 – Systems of Equations & Inequalities:
Inequalities: Sample Unit Outline
TOPIC
HOMEWORK
DAY 1
Solving Systems of Equations by Graphing
HW #1
DAY 2
Solving Systems of Equations by Substitution
HW #2
DAY 3
More Practice with Graphing vs. Substitution Methods
DAY 4
Quiz 5-1
DAY 5
Solving Systems of Equations by Elimination (Day 1)
HW #3
DAY 6
Solving Systems of Equations by Elimination (Day 2)
HW #4
DAY 7
Comparing Methods to Solving Systems
HW #5
DAY 8
Word Problems
HW #6
DAY 9
Quiz 5-2
None
None
DAY 10
Solving Systems by Matrices
HW #7
DAY 11
Linear Inequalities
HW #8
DAY 12
Systems of Linear Inequalities
HW #9
DAY 13
Quiz 5-3
DAY 14
Systems of Linear Inequalities Word Problems
HW #10
DAY 15
Review for Test; Complete Study Guide
HW #11
DAY 16
UNIT 5 TEST
None
None
See sample images of the pages on the next page.
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name:
Date:
___________________________________________________
_________________________________
Topic:
Class:
___________________________________________________
_________________________________
Main Ideas/Questions
Notes/Examples
SYSTEMS OF
EQUATIONS
The SOLUTION
to a System
TYPES OF
SOLUTIONS
Graphically: The point (x, y) where the two lines ____________________.
Algebraically: The point (x, y) that makes both equations ______________.
INTERSECTING LINES
PARALLEL LINES
SAME LINE
ONE SOLUTION
NO SOLUTION
INFINITE SOLUTION
SOLVING
SYSTEMS BY
GRAPHING
Directions: Solve each system of equations by graphing.
y = x − 8
1. 
 y = −2 x + 1
1

y = x + 9
2. 
2
 y = − x + 6
y
y
x
Solution:
x
Solution:
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
 −3 x + y = 8
3. 
 − x + y = −2
x + 2y = 4

4. 
1
 y = − 2 x + 2
y
y
x
x
Solution:
Solution:
 x + 3 y = −15
5. 
 y = −7
y = x + 5
6. 
x − y = 2
y
y
x
x
Solution:
Solution:
3 x − 5 y = −35
7. 
2 x + y = −6
 x = −2
8. 
3 x − 2 y = −18
y
y
x
Solution:
x
Solution:
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 1: Solving Systems by Graphing
** This is a 2-page document! **
Solve each system of equations by graphing. Clearly identify your solution.
2

y = x −1
1. 
3
 y = − x + 4
x − y = 7
2. 
 x − y = −4
y
y
x
x
y = x −1
3. 
 x + 4 y = 16
5 x + 2 y = 4
4. 
9 x + 2 y = 12
y
y
x
2 x − 6 y = 30

5. 
1
 y = 3 x + 1
x
5 x + 4 y = −12
6. 
3 x − 4 y = −20
y
x
y
x
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
x − y = 1
7. 
y = 5
 y = −2 x − 1
8. 
3 x − 4 y = −40
y
y
x
3 x − 2 y = −16
9. 
 x + y = −7
x
2 x + y = 8
10. 
x = 5
y
y
x
x
Questions:
1) If a system of linear equations has one solution, what does this mean about the two lines?
2) If a system of linear equations has no solution, what does this mean about the two lines?
3) If a system of linear of linear equations has infinitely many solutions, what does this mean about
the two lines?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Entrance Ticket
Name: _________________________________________
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
1) Describe the three possible solutions to a system of equations.
Solve the following systems of equations by graphing:
2) 3x + 2y = -8
x – y = -1
Entrance Ticket
3) x – 4y = 8
1
y= x+3
4
Name: _________________________________________
Solve the following systems of equations by graphing:
2) 3x + 2y = -8
x – y = -1
3) x – 4y = 8
1
y= x+3
4
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
1) Describe the three possible solutions to a system of equations.
Name:
Date:
___________________________________________________
_________________________________
Topic:
Class:
___________________________________________________
_________________________________
Main Ideas/Questions
Notes/Examples
Substitution
Method
Steps to Solve
•
Step 1: Solve one equation for ______ or ______.
•
Step 2: __________________________ this expression into the other
equation and ______________ for the variable.
•
Step 3: ____________________ your answer into the revised equation
from Step 1 and ________________ for the other variable.
Examples
Directions: Solve each system by substitution.
y = 4x −1
1. 
 y = 2x − 5
 y = 6x
2. 
2 x + 3 y = −20
y = x + 9
3. 
 3 x + 8 y = −5
x = 4 y + 7
4. 
2 x − 6 y = 12
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
 2 x + y = −2
5. 
5 x + 3 y = −8
2 x − 3 y = −11
6. 
2 x + y = 9
x + 5 y = 4
7. 
3 x + 15 y = −1
x + 4 y = 0
8. 
3 x + 2 y = 20
6 x + 3 y = 54
9. 
2 x + y = 18
 x − 3 y = −2
10. 
10 x + 8 y = −20
 3 x − y = −8
11. 
5 x + 2 y = 5
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Graphing
1
y=x+6
y = -2x – 3
VS.
substitution
y=x+6
y = -2x – 3
2 5x – y = -5
3x – 6y = 24
5x – y = -5
3x – 6y = 24
3 2x – 3y = -12
x+y=9
2x – 3y = -12
x+y=9
4 x – 3y = -15
x = -3
x – 3y = -15
x = -3
5 y = 2x – 4
6x – 3y = 12
y = 2x – 4
6x – 3y = 12
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
6 2x + y = -8
3x – 5y = -25
2x + y = -8
3x – 5y = -25
7 2x + 9y = 27
x – 3y = -24
2x + 9y = 27
x – 3y = -24
8 x – 2y = 8
8x + 6y = 42
x – 2y = 8
8x + 6y = 42
9 2x – 2y = 14
x–y=2
2x – 2y = 14
x–y=2
10 x = 4y
x + 2y = 12
x = 4y
x + 2y = 12
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
I
SYSTEMS OF EQUATIONS!
Solve each system of equations by substitution or elimination. Partner A should do the left side and
Partner B should do the right side. After each set of problems, check answers with each other.
Identify your matching answers, and color the hearts accordingly.
Partner A: ____________________
_________________
Partner B: ______________
______________________
 2 x − 5 y = −22
1. 
 x + 7 y = 27
____________________
 y = −3 x + 5
Red: 
 3 x − 2 y = −10
__________________
 y = −3 x − 13
2. 
 9 x − 2 y = −4
____________________
 x + 6 y = −7
Orange: 
 2 x + 12 y = −14
__________________
 x + y = 15
3. 
 4 x + 4 y = 10
____________________
Yellow:
 x − 3 y = −15
4. 
 2x + y = 5
____________________
 5 x − 4 y = 18
Light Green: 
 x + y = −9
__________________
 x − 2 y = −8
5. 
6x + 7 y = 9
____________________
 x − 3 y = 22
Dark Green: 
 8 x − 6 y = 14
__________________
 x + 2 y = −9
6. 
 5 x + 6 y = −13
____________________
6x − 3y = 9
Light Blue: 
 y = 2x − 5
__________________
 3 x + y = 19
7. 
 4 x − 8 y = 16
____________________
 4 x + y = 20
Dark Blue: 
 x + 3 y = −17
__________________
 x − 4 y = 31
8. 
 x− y =4
____________________
 x − y = −5
Purple: 
4x + 3y = 8
__________________
 3 x − 5 y = −12
9. 
 y = −x − 4
____________________
Pink:
 2 x + 6 y = −28
10. 
 x + 3 y = −14
____________________
 5 x + 8 y = 14
White: 
 − 3x + y = 9
1
.) HOT
STUFF
6
CALL
.)
ME
2
.)YOU’RE
MINE
7
.) YOU
ROCK
3
.) TEXT
ME
8
.) XOXO
XOXO
 y = x −5

 x − 7 y = −1
 x + 8 y = −4

 5 x + 4 y = −20
4
.) LOVE
BUG
9
.)SWEET
PEA
__________________
__________________
__________________
5
.)
BE
MINE
10
.) PUPPY
LOVE
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 2: Solving Systems by Substitution
** This is a 2-page document! **
Solve each system of equations by substitution. Clearly identify your solution.
 y = 3 x + 19
1. 
 y = 5 x + 33
 y = −2 x + 2
2. 
 y = 7 x + 11
y = x + 8
3. 
x + y = 2
 y = 2x
4. 
5 x − y = 9
y = x + 2
5. 
3 x + 3 y = 6
x = 3y
6. 
2 x + 4 y = 10
 y = 2x + 1
7. 
2 x − y = 3
3 x − 7 y = 41
8 
 x = −2 y − 21
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
5 x + 2 y = 7
9. 
4 x + y = 8
x − 2y = 3
10. 
 4 x − 8 y = 12
 2 x + y = −2
11. 
5 x + 3 y = −8
2 x − 3 y = −24
12. 
 x + 6 y = 18
 8 x − y = −6
13. 
2 x − 3 y = 4
 x + 2 y = −2
14. 
3 x + 4 y = 6
 x − 3 y = 16
15. 
4 x − y = 9
 x − y = −10
16. 
2 x + 4 y = 22
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _____________________________________
Algebra I
Date: ___________________________ Bell: ______
Unit 5: Systems of Equations & Inequalities
Quiz 5-1: Solving Systems by Graphing & Substitution
For questions 1 – 2, solve the system by graphing.
3 x + y = 5
y = x + 4
1. 
 x − 4 y = 32
ANSWERS
2. 
x − y = 1
1. ___________
y
y
2. ___________
3. ___________
4. ___________
x
x
5. ___________
6. ___________
For questions 3 – 6, solve the system using the substitution method.
 y = −2 x
3. 
7 x − 8 y = −23
x − 2y = 1
5. 
3 x − 6 y = 3
3 x + y = 13
4. 
5 x − 2 y = 18
6 x − y = −23
6. 
 8 x + 3 y = −9
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name:
Date:
___________________________________________________
_________________________________
Topic:
Class:
___________________________________________________
_________________________________
Main Ideas/Questions
Notes/Examples
Elimination
Method
Steps to
Solve
•
Step 1: Make sure the equations are lined up!
•
Step 2: ___________ or ___________________ the equations to eliminate
the variable with common _____________________________.
•
Step 3: __________________ for the remaining variable.
•
Step 4: _______________________ your answer into either original
equation and _______________ for the other variable.
Examples
Directions: Solve each system by elimination.
 y = 3x + 4
1. 
y = x − 2
 x + 4 y = 13
2. 
x − y = 3
3.
3 x − 10 y = 14

3 x − 9 y = 15
4 x + 2 y = 6
4. 
 −2 x + 2 y = 18
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
5.
4 x + 9 y = 5

 −4 x + 7 y = 11
10 x − 3 y = 18
6. 
 −2 x + 3 y = 6
 x − y = 10
7. 
3 x + y = 18
 x = 3 y + 11
8. 
2 x − 3 y = 16
4 y = 2 x − 8
9. 
5 x − 4 y = 20
3 x − 4 y = −10
10. 
3 x − 4 y = −13
2 x + y = −10
11. 
 − y = 2 x + 10
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 3: Solving Systems by Elimination
(Day 1)
** This is a 2-page document! **
Solve each system of equations by elimination. Clearly identify your solution.
 y = −x + 1
1. 
 y = 4 x − 14
3.
 x − 2 y = 10

x + 3y = 5
 y = −3 x + 5
2. 
 y = −8 x + 25
 2x − 3y = 9
4. 
 −5 x − 3 y = 30
 x + y = −4
5. 
x − y = 2
2 x − 3 y = 14
6. 
 x + 3 y = −11
 −3 x − 4 y = − 1
7. 
 3 x − y = −4
8.
6 x + 5 y = 4

6 x − 7 y = −20
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
3 x − 4 y = −14
9. 
 3 x + 2 y = −2
6 x − 3 y = 12
10. 
 4 x − 3 y = 24
5 x = y + 6
11. 
5 x + 2 y = 3
2 x − y = −22
12. 
 y = 7 x + 67
6 x − 3 y = −21
13. 
4 x = 3 y − 9
 4 y = −3 − x
14. 
7 x − 4 y = 43
x + 3y = 5
15. 
 x = −6 y + 14
 −2 x − y = 12
16. 
 y = −26 − 9 x
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name:
Date:
___________________________________________________
_________________________________
Topic:
Class:
___________________________________________________
_________________________________
Main Ideas/Questions
Notes/Examples
What if there are
no common
coefficients?
EXAMPLES
x + 3 y = 6
1. 
2 x − 7 y = −1
9 x + 3 y = 12
2. 
2 x + y = 5
3 x − y = 14
3. 
5 x + 4 y = 12
 x + y = −3
4. 
5 x − 2 y = −50
3 x − 3 y = −3
5. 
2 x − y = −5
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
3 x + y = 2
6. 
6 x + 2 y = 4
3 x + 4 y = 6
7. 
7 x + 8 y = 10
3 x + 3 y = 9
8. 
5 x + 4 y = 10
5 x + 9 y = −10
9. 
7 x + 10 y = −1
2 x = 4 y + 18
10. 
 −5 x − 6 y = 3
2 x + 4 y = 6
11. 
3 x = 12 − 6 y
7 x + 5 y = −13
12. 
 −2 x = 7 y + 26
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 4: Solving Systems by Elimination
(Day 2)
** This is a 2-page document! **
Solve each system of equations by elimination. Clearly identify your solution.
 x − 2 y = 12
1. 
5 x + 3 y = −44
7 x − 2 y = 37
2. 
 4 x + y = 19
 3 x + 8 y = −5
3. 
 −2 x + 2 y = 18
x − 3y = 7
4. 
2 x − 6 y = 12
 2 x + y = −2
5. 
5 x + 3 y = −8
2 x + 5 y = 14
6. 
 4 x + 2 y = −4
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
2 x − 6 y = 12
7. 
 −5 x + 15 y = −30
5 x + 2 y = −3
8. 
3 x + 3 y = 9
3 x + 2 y = −26
9. 
 4 x − 5 y = −4
10.
 4 x + 3 y = −1

5 x + 4 y = 1
2 x + 3 y = 6
11. 
2 y = 5 − x
12.
3 x = 2 y − 7

2 x − 5 y = 10
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
GROUP MEMBERS:
PERIOD: _______
Comparing Methods to Solving Systems
Systems of equations can be solved by graphing, substitution, or elimination. However,
there are situations where one method may be more sophisticated than another. Solve
the following systems using the graphing, substitution, or elimination method.
You may only use each method once.
SYSTEM A
Method of Choice: ______ Graphing _____ Substitution _____ Elimination
 x − y = −2

 7 x + 2 y = −5
Solution:
SYSTEM B
Method of Choice: ______ Graphing _____ Substitution _____ Elimination
8 x + 5 y = −13

3 x + 4 y = 10
Solution:
SYSTEM C
Method of Choice: ______ Graphing _____ Substitution _____ Elimination
 4 x − 3 y = 18

2 x + y = 4
Solution:
Answer the following question on a separate sheet of paper:
What is your reasoning for picking the method for each system?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
SYSTEMS OF EQUATIONS REVIEW
Solve each system of equations by GRAPHING. Clearly identify your solution.
x + y = 3
x + 2 y = 6
1. 
2. 
x = 4
3 x + 2 y = 14
Solve each system of equations by SUBSTITUTION. Clearly identify your solution.
 y = 7x + 6
 x − 7 y = −21
3. 
4. 
−
=
4
x
3
y
16
2 x − 14 y = −42

3 x − 5 y = 15
5. 
 x − 4 y = 12
 y = −5
6. 
8 x + 5 y = −17
Solve each system of equations by ELIMINATION. Clearly identify your solution.
 x − y = −10
2 x + 2 y = 28
7. 
8. 
8 x − 2 y = 22
 x − 6 y = −25
3 x + 6 y = 27
9. 
 x + 2 y = 11
 4 x + 5 y = 22
10. 
7 x − 3 y = −32
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 5: Solving Systems – All Methods
** This is a 2-page document! **
Solve each system of equations by GRAPHING. Clearly identify your solution.
4 x − y = 3
1. 
3 x + y = 4
5 x + 2 y = 4
2. 
3 x + 6 y = −12
y
y
x
x
2 x + y = 1
3. 
 x − 2 y = 18
x − 3y = 3
4. 
2 x − 6 y = −24
y
y
x
x
Solve each system of equations by SUBSTITUTION. Clearly identify your solution.
x + 3y = 9
5. 
 4 x − 2 y = −6
2 x + 5 y = −7
6. 
 7 x + y = −8
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
 x − 3 y = −24
7. 
5 x + 8 y = −5
5 x + 3 y = 15
8. 
x − 6 y = 3
Solve each system of equations by ELIMINATION. Clearly identify your solution.
 x + y = −5
9. 
x − y = 9
 x + 5 y = 20
10. 
2 x − 7 y = −45
 4 x + 3 y = −1
11. 
5 x + 4 y = 1
x = 2y − 3
12. 
 2 x − 3 y = −5
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
SYSTEMS OF EQUATIONS Applications
Many real world problems can be modeled and solved using a
system of equations. Use the process below to solve these problems.
1
DEFINE
YOUR TWO
VARIABLES
2
WRITE A SYSTEM OF
EQUATIONS using the
given information.
3
4
SOLVE THE
SYSTEM!
ANSWER IT!
Give exactly what the
problem is asking for.
1. The sum of two numbers is 30 and their
difference is 12. Find the two numbers.
2. The sum of two numbers is 24 and their
difference is 2. What are the numbers?
3. The difference between two numbers is 9.
The first number plus twice the other number
is 27. Find the two numbers.
4. The sum of two numbers is 36. Twice the first
number minus the second is 6. Find the
numbers.
5. The sum of two numbers is 20. The difference
between three times the first number and
twice the second is 40. Find the two
numbers.
6. The sum of two numbers is 25. One number
is twice the second number plus seven.
What are the two numbers?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
7. The cost of 3 boxes of envelopes and 4 boxes of notebook paper is $13.25. Two boxes of
envelopes and 6 boxes of notebook paper cost $17. Find the cost of each.
8. The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the
cost of each.
9. Gabby and Sydney bought some pens and pencils. Gabby bought 4 pens and 5 pencils for
$6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost of each.
10. At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tori
bought two pairs of gloves and two hats for $30.00. Find the cost of each.
11. A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and
the larger mower cost $329.99. If 30 total mowers were sold and the total sales for a given
year was $8379.70, find how many of each type were sold.
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
12. The Town Recreation Department ordered a total of 100 baseballs and bats for the summer
baseball camp. Baseballs cost $4.50 each and bats cost $20 each. The total purchase was
$822. How many of each item was ordered?
13. A group of 40 children attended a baseball game on a field trip. Each child received either
a hot dog or bag of popcorn. Hot dogs were $2.25 and popcorn was $1.75. If the total bill
was $83.50, how many hotdogs and bags of popcorn were purchased?
14. One night a theater sold 548 movie tickets. An adult’s ticket costs $6.50 and a child’s ticket
cost $3.50. In all, $2881 was taken in. How many of each kind of ticket were sold?
15. Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. On a
given night, 321 tickets were sold for $937.50. How many of each kind of ticket were sold?
16. A collection of dimes and nickels is worth $3.30. If there are 42 coins in all, how many of each
kind of coin are there?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
17. Mary has a collection of nickels and quarters for a total value of $4.90. If she has 42 coins
total, how many of each kind are there?
18. Rob has $1.65 in nickels and dimes. He has 25 coins in all. How many of each kind of coin are
there?
19. Your math teacher tells you that the next test is worth 100 points and contains 38 problems.
Multiple-choice questions are worth 2 points each and word problems are worth 5 points.
How many of each type of question are there?
20. Ms. Miller decides to give a test worth 90 points and contains 25 questions. Multiple-choice
questions are worth 3 points and word problems are worth 4 points. How many of each type
of question are there?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Good Work! ☺
Name: ________________________________
Date: ______________________ Bell: ______
Unit 5: Systems of Equations & Inequalities
Homework 6: Systems Word Problems
** This is a 2-page document! **
Solve each word problem using a system of equations. Use substitution or elimination.
1. One number added to three times another number is 24. Five times the first number added to
three times the other number is 36. Find the numbers.
2. Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large
cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each
type did she sell?
3. Your family goes to a Southern-style restaurant for dinner. There are 6 people in your family.
Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill
was $99, how many people ordered each dinner?
4. Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8
tickets for $52.75. How many adult tickets and student tickets were purchased?
5. A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 12
gloves were sold for a total of $561. Right-handed gloves cost $45 each and left-handed gloves
cost $52 each. How many of each type of glove were sold?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
6. David bought 3 DVDs for 4 books for $40 at a yard sale. Anna bought 1 DVD and 6 books for
$18. How much did each DVD and book cost?
7. Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a
flight had 52 passengers who paid $1360, how many first class and tourist class passengers were
there?
8. Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many of each kind
of coin does she have?
9. At the Holiday Valley Ski Resort, skis cost $16 to rent and snowboards cost $19. If 28 people
rented on a certain day and the resort brought in $478, how many skis and snowboards were
rented?
10. Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised $43.50
by selling 12 rolls of solid paper and 9 rolls of printed paper. Joel raised $51.50 by selling 8 rolls
of solid cost of paper and 15 rolls of printed paper. Find the cost of each type of wrapping
paper.
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _____________________________________
Algebra I
Date: ___________________________ Bell: ______
Unit 5: Systems of Equations & Inequalities
Quiz 5-2: Solving Systems (All Methods) – Including Word Problems
For questions 1 and 2, solve the system by GRAPHING.
 x − y = −9
1. 
3 x + 4 y = 8
ANSWERS
 3 x − y = −1
2. 
 x − 2 y = −12
y
1. ____________
y
2. ____________
3. ____________
4. ____________
x
x
5. ____________
6. ____________
For questions 3 and 4, solve the system using the SUBSTITUTION method.
2 x − 7 y = 13
3. 
3 x + y = 8
x − 3y = 2
4. 
2 x − 6 y = 6
For questions 5 and 6, solve the system using the ELIMINATION method.
x + y = 3
5. 
 x − 3 y = −29
3 y = 26 − 5 x
6. 
6 x + 7 y = 21
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
For Questions 7 – 10, define the variables and set up a system of equations.
Solve by substitution or elimination. Clearly give your answer.
7. Two times a number added to another number is 25. Three times the first number minus the
other number is 20. Find the numbers.
8. At a baseball game, Henry bought 5 hotdogs and 3 bags of chips for $14.82. Scott bought 7
hotdogs and 6 bags of chips for $22.89. Find the cost of each hotdog and bag of chips.
9. Disney held a breakfast for parents and their children to eat with Mickey Mouse. Adult tickets cost
$17.95 and children’s tickets cost $12.95. Disney made $7355 from ticket sales from a total of 500
people that attended. How many adults and how many children were at the breakfast?
10. Gabe has 60 coins consisting of quarters and dimes. The combined value of the coins is $9.45.
How many quarters and dimes does Gabe have?
BONUS: Create a system of equations with a solution of (-5, 2)
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name:
Date:
___________________________________________________
_________________________________
Topic:
Class:
___________________________________________________
_________________________________
Main Ideas/Questions
Notes/Examples
Solving Systems
with Matrices
Steps to Solve
• Step 1: Make sure both equations are in standard form.
• Step 2: Rewrite the system as a matrix and enter into your calculator.
a. 2ND, x-1
b. Arrow over to EDIT, ENTER
c. Enter the dimensions of the matrix as 2 x 3
d. Enter the system as a matrix
• Step 3: Clear the screen by hitting 2ND, MODE
• Step 4: Solve the system using calculator
a. 2ND, x-1
b. Arrow over to MATH
c. Select Option B: rref(, then hit ENTER
d. 2ND, x-1 and choose the appropriate matrix, ENTER, ENTER
Examples
Directions: Solve the following systems of equations using matrices.
 x + y = 13
1. 
2 x − 3 y = 1
x + y = 2
2. 
x − y = 6
 9 x + 2 y = −5
3. 
3 x − y = −10
2 x − 5 y = 19
4. 
 y = 4 x − 11
 −4 x − 8 y = 23
5. 
 x + 2 y = 13
 x = −6 y
6. 
 4 x + 7 y = −17
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
x + y = 2
7. 
2 x + y = −1
8 x − 6 y = 84
8. 
 4 x − 42 = 3 y
2 x + 7 = 9 y
9. 
x = 5 y − 3
 −5 x = 9 y − 20
10. 
6 x + 8 y = 24
11. Two families go to a hockey game. One family purchases two adult tickets
and four youth tickets for $33. Another family purchases four adult tickets
and five youth tickets for $51.75. What is the cost of an adult ticket and the
cost of a youth ticket?
12. Bob has 60 coins consisting of quarters and dimes. The coins combined
value is $13.35. How many quarters and how many dimes does he have?
13. The next Algebra test is worth 100 points and contains 35 problems. Multiplechoice questions are worth 2 points each and word problems are 7 points
each. How many of each type of equation are there?
14. On one day Fred’s Sports World sold 9 Buffalo Bills jerseys and 3 Miami Dolphin
jerseys for a total of $899.40. The next day they sold 12 Bills jerseys and only 2
Dolphins jerseys for a total of $1139.30. How much is the Bills jersey and how
much is the Dolphins jersey?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________
Date: _______________________ Bell: ______
Unit 5: Systems of Equations & Inequalities
Homework 7: Solving Systems Using Matrices
Solve each system of equations using matrices. Clearly give the matrix and solution.
10 x + 12 y = 6
 −8 x + 2 y = −8
2. 
1. 
16
x
6
y
24
+
=
−
7 x − 3 y = −30

 −20 x + 6 y = −26
3. 
10 x − 3 y = 6
3 x − 5 y = −14
4. 
 4 x + y = 12
 −4 x − 3 y = 15
5. 
 −2 x − 6 y = 12
 −2 x − 3 y = −9
6. 
10 x + 6 y = −18
2 x + 6 y = −10
7. 
 −4 x = 12 y + 20
 −2 x = −6 y + 8
8. 
2 y = x + 1
12 x + 30 = −9 y
9. 
 −6 x − 26 = 10 y
3 y + 1 = 4 x
10. 
 −10 y = 12 x − 22
11. The price of a cellular telephone plan is based on peak and nonpeak service. Kelsey used 45 peak
minutes and 50 nonpeak minutes and was charged $27.75. That same month, Mitch used 70 peak
minutes and 30 nonpeak minutes and was charged $36. What are the rates per minute for peak
and nonpeak time?
12. Steven has a collection of nickels and dimes. In all, he has 17 coins. The total value of the collection
is $1.15. How many nickels and how many dimes does he have?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name:
Date:
___________________________________________________
_________________________________
Topic:
Class:
___________________________________________________
_________________________________
Main Ideas/Questions
Notes/Examples
LINEAR
INEQUALITY
SOLUTION
to a Linear Inequality
EXAMPLE
Determine which ordered pairs are solutions to the linear inequality below:
2 x − 3 y < 15
(2, 5)
(3, -4)
(0, 0)
Step 2
Step 1
Graphing linear inequalities is a way to show ALL the
ordered pairs that are solutions! Steps to graph:
Put the inequality in _____________- _______________________ form.
Be sure to flip the inequality symbol if you multiply or divide by a
negative number!
Graph the line!
•
Use a ___________________ line for _____ or _____ symbols.
•
Use a ___________________ line for _____ or _____ symbols.
Shade!
Step 3
GRAPHING
Linear Inequalities
(-1,- 7)
•
Shade _____________ the line for _____ or _____ symbols.
•
Shade _____________ the line for _____ or _____ symbols.
Example: 2 x − 3 y < 15
y
x
© Gina Wilson (All Things Algebra®, LLC), 2016
Directions: Graph each linear inequality to show all possible solutions.
2. y ≤ −2 x − 1
1
1. y > x − 5
3
3. 5 x − 2 y > 12
4. x − 4 y < 8
5. x − y ≥ 8
6. 3 x + 2 y < 0
7. y ≤ −4
8. x > 7
© Gina Wilson (All Things Algebra®, LLC), 2016
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 8: Linear Inequalities
** This is a 2-page document! **
Graph each linear inequality to show all possible solutions.
5
1
1. y ≤ x − 4
2. y > − x + 7
y
3
2
y
x
x
3. 2 x + y < 1
4. 2 x − 5 y ≥ 30
y
y
x
x
5. x − y > 5
6. 2 x − 6 y ≤ −24
y
x
y
x
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
7. x − 4 y < 0
8. 2 x + 7 y ≤ −7
y
y
x
9. 5 x − 4 y ≥ 28
x
10. 12 x + 8 y < 24
y
y
x
x
12. y ≤ 1
11. x > −6
y
y
x
x
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Entrance Ticket
Name: _________________________________________
Graph the following linear inequalities:
“
2) 3x – 2y ≥ 8
Identify the linear inequality shown on the graph.
3)
4)
A. 2x + 5y > -5
A. 4x + y ≥ 2
B. 2x – 5y < 5
B. x + 4y ≤ 8
C. 5x + 2y > -2
C. 4x – y ≥ -2
D. 5x – 2y < 2
D. x – 4y ≤ -8
Entrance Ticket
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
1) y ≤ -2x + 1
Name: _________________________________________
Graph the following linear inequalities:
“
2) 3x – 2y ≥ 8
Identify the linear inequality shown on the graph.
3)
A. 2x + 5y > -5
4)
A. 4x + y ≥ 2
B. 2x – 5y < 5
B. x + 4y ≤ 8
C. 5x + 2y > -2
C. 4x – y ≥ -2
D. 5x – 2y < 2
D. x – 4y ≤ -8
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
1) y ≤ -2x + 1
Name:
Date:
___________________________________________________
_________________________________
Topic:
Class:
___________________________________________________
_________________________________
Main Ideas/Questions
Notes/Examples
Systems of
Linear Inequalities
SOLUTION
to a System of
Linear Inequal
Inequalities
Directions: Graph each system of linear inequalities to show all possible solutions.
 y > −x − 1
1. 
y < x − 5
1

y < x + 7
2. 
3
 y ≥ − x + 4
y
y
x
x
 x − 4 y ≤ 24
3. 
 y ≤ 2x + 1
 x < −4
4. 
 3 x + 2 y ≤ −2
y
y
x
x
 4 x − 5 y ≥ −35
5. 
 y > −x − 2
6 x + 4 y > 12
6. 
3 x − 4 y > 8
y
x
y
x
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
 y < −5 x + 6
7. 
 y ≥ 2x − 1
8 y > −10 x + 24
8. 
y ≤ 2
y
y
x
3 x − y < 6
9. 
 3 x − y > −2
x
5 x + 2 y ≥ 4
10. 
 x + 4 y < −8
y
y
x
7 x + 4 y ≥ −32
11. 
 x − y < −3
x
 x − 2 y ≥ 12
12. 
 x + 2 y ≤ −8
y
y
x
x
Application: Sarah’s Pet Store never has more than a combined total of 16 cats and dogs. She
also never has more than 9 cats. Write a system of inequalities and graph to show the possible
number of cats and dogs in her store.
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: __________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 9: Systems of Inequalities
** This is a 2-page document! **
Graph each system of inequalities to show all possible solutions.
 y > −2 x + 5
1. 
y ≤ x − 3
2

y ≤ − x − 3
2. 
3
 y ≥ 3 x + 8
5 x − 6 y > 42
3. 
3 x + 2 y ≤ 14
7 x + 3 y ≤ −24
4. 
 x + 3 y ≤ −6
x − y > 3
5. 
x ≥ 6
 y < 2x + 5
6. 
2 x − y ≤ 3
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
 x + 3 y < −18
7. 
5 x + 2 y ≤ 14
 y ≥ −1
8. 
5 x + 3 y > −18
 x − 2 y < −16
9. 
x + y ≥ 5
 x − y < −6
10. 
x − y ≤ 1
 x − 3 y ≥ 12
11. 
2 x − y ≥ −6
2 x + 5 y > 20
12. 
2 x + 5 y < −5
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Entrance Ticket
Name: _________________________________________
Solve the following systems of inequalities by graphing:
1. 3x + 4y < 28
2. Which of the following points are solutions to the system above?
a. (1, 3)
b. (3, -4)
Entrance Ticket
c. (0, -5)
d. (-2, 0)
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
x – 2y ≤ 0
Name: _________________________________________
Solve the following systems of inequalities by graphing:
1. 3x + 4y < 28
2. Which of the following points are solutions to the system above?
a. (1, 3)
b. (3, -4)
c. (0, -5)
d. (-2, 0)
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
x – 2y ≤ 0
More with Linear Inequalities
.
1) Which ordered pair is a solution to the linear
inequality below?
2) Which ordered pair is a solution to the linear
inequality below?
x + 4y < 4
3x – 5y ≥ 10
A. (1, 4)
A. (-3, 5)
B. (6, -3)
B. (0, 4)
C. (-5, -2)
C. (2, 3)
D. (2, 0)
D. (-8, -2)
3) Which ordered pair is a solution to the linear
inequality below?
2x – 3y < 9
4) Which ordered pair is a solution to the linear
inequality below?
y ≥ -2x + 7
A. (6, -4)
A. (-1, 5)
B. (-1, -9)
B. (3, 2)
C. (2, -5)
C. (2, -8)
D. (-3, -3)
D. (-4, 0)
5) Identify the ordered pairs that are solutions to the linear inequality 5x – y > 4?
(-2,(4,
1)2)
(
(-2,(-3,
1) 1)
(
(-2,(5,1)-2)
(
(-2, (2,
1) 7)
(
(-2,(0,1)-1)
(
(-2, (8,
1) 4)
(
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
6) Which ordered pair is in the solution set of the following system of inequalities?
 2 x + 4 y ≤ 12

 3x − y < 2
A. (-3, 2)
B. (6, 4)
C. (-1, -7)
D. (5, -2)
7) Which ordered pair is in the solution set of the following system of inequalities?
 y < 2x + 2

 y ≥ −x +1
A. (0, 5)
B. (2, 0)
C. (-1, -3)
D. (-6, 4)
8) Which ordered pair is in the solution set of the following system of inequalities?
 3 x + 4 y > 12

 y > 2x − 1
A. (3, -5)
B. (6, 0)
C. (-8, -1)
D. (-2, 6)
9) Which ordered pair is in the solution set of the following system of inequalities?
 y ≤ 3x + 1

 x− y>1
A. (-1, 4)
B. (4, 5)
C. (-3, -6)
D. (7, -2)
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _____________________________________
Algebra I
Date: ___________________________ Bell: ______
Unit 5: Systems of Equations & Inequalities
Quiz 5-3: Linear Inequalities & Systems of Inequalities
Graph the following linear inequalities.
1. y ≤ -2x + 1
2. 2x – 5y < 20
3. x – 3y < 0
Select the inequality that best represents the graph.
4.
A. x + y ≤ -4
B. x + y ≥ -4
C. x – y ≤ 4
D. x – y ≥ 4
5.
A. x < -2
B. y < -2
C. x > -2
D. y > -2
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Graph the following systems of linear inequalities.
6. x + y > 8
x>5
7. 4x + y ≥ 4
3x – 2y > 14
Use the graph to determine which ordered pair is a solution to the system of inequalities.
8. y < 2x + 1
y ≤ -3x + 4
A. (1, -4)
B. (1, 5)
C. (-3, 4)
D. (3, 0)
9. x – 2y > -8
x+y≥1
A. (-5, 3)
B. (0, 5)
C. (3, -5)
D. (4, 0)
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Systems of Inequalities
WORD PROBLEMS
1. Suppose you buy flour and cornmeal in bulk to make flour tortillas and corn tortillas. Flour costs
$1.50 per pound and cornmeal costs $2.50 per pound. You want to spend less than $25 on flour
and cornmeal, but you need at least 6 pounds altogether.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
2. A seafood restaurant owner orders perch and salmon. Perch is $4/lb and salmon is $3/lb. He wants
to buy at least 50 pounds of fish but cannot spend more than $240.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
3. The “We Sell CDs” website plans to purchase ads in a local newspaper to advertise their site. Their
operating budget will allow them to spend at most $3000 on this advertising adventure. An ad will
cost $30 to appear in the weekday paper and $50 to appear in the weekend edition. They plan to
run at least 20 ads.
4. Mary knits scarves and sweaters to sell. Scarves take 2 hours to knit and sweaters take 10 hours.
Mary would like to spend no more than 40 hours per week knitting and knit at least 5 items per
week.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
5. A clothing store has a going-out-of business sale. They are selling pants for $8.99 and shirts for
$3.99. You can spend as much as $60 and want to buy at least two pairs of pants.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
6. You’d like to see how many baseball and soccer games you can attend this spring. Travel time for
baseball games is 2 hours and soccer games is 1 hour. You would like to spend no more than 15
hours traveling to the games. In total, you would like to attend at least 8 games.
______________________________
_____________________________
c. Suppose we decide on attending 4 baseball games,
what is the range of soccer games you can attend?
d. Suppose we decide on attending 9 soccer games,
what is the range of baseball games you can attend?
e. Is it possible to attend 6 baseball games and
4 soccer games?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
a. Write and graph a system of linear inequalities:
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 10: Systems by Inequalities –
Word Problems
** This is a 2-page document! **
1. Emily wants to buy turquoise stones on her trip to New Mexico to give to at least 4 of her friends. The
gift shop sells small stones for $4 and large stones for $6. Emily has no more than $30 to spend.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
2. Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an
hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
3. A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and
common nails cost $0.60 per pound. He would like to purchase at least 30 pounds of nails total.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
4. A local ’theater has a maximum capacity of 1,000 people. For their latest production, adult tickets cost
$25 and youth tickets cost $12.50. The theater must make at least $15,000 for the show to go on.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
5. A zoo keeper wants to fence a rectangular habitat for goats. The length of the habitat should be
at least 80 feet, and the perimeter of the habitat should be more no more than 300 feet.
a. Write and graph a system of linear inequalities:
______________________________
_____________________________
b. Write two possible solutions:
i. _______________
ii. _______________
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Unit 5 Test Study Guide
Name: _________________________________________
(Systems of Equations & Inequalities)
Date: ____________________________ Per: __________
Topic 1: Solving Systems of Equations by Graphing
Solve each system of equations by graphing.
x + y = 2
1. 
x − y = 4
3 x − 5 y = 15
2. 
 y = 2x + 4
y
y
x
x
 x − 4 y = 28
3. 
 x + 2 y = −2
3 y = 4 x − 6
4. 
8 x − 6 y = −30
y
x
y
x
Topic 2: Solving Systems of Equations by Substitution
Solve each system of equations by substitution.
 y = 2x + 3
5. 
 y = −x − 9
2 x + 3 y = 4
6. 
 y = 5 x − 27
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
 x + 4 y = 19
7. 
x − 2y = 1
6 x − y = −21
8. 
5 x + 3 y = 17
Topic 3: Solving Systems of Equations by Elimination
Solve each system of equations by elimination.
 x − 3 y = −13
9. 
3 x + 7 y = 25
2 x + 8 y = 6
10. 
5 x + 20 y = 15
7 x − y = 19
11. 
2 x − 3 y = 19
 4 x − y = −4
12. 
5 x = 2 y + 1
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Topic 4: Systems of Equations Applications
Define variables, set up a system of equations, then solve by substitution elimination.
13. A tennis coach took his team out for lunch and bought 8 hamburgers and 5 fries for $24. The
players were still hungry so the coach bought 6 more hamburgers and 2 more fries for $16.60.
Find the cost for one hamburger.
14. Jim sells hot dogs for $2.95 each and steak sandwiches for $9.95 each out of his food cart.
During a busy outdoor festival, he sold a total of 985 items for $7343.75. How many steak
sandwiches did he sell?
15. Bob bought 24 hockey tickets for $83. Adult tickets cost $5.50 and child tickets cost $2.00.
How many child tickets did he buy?
16. Ethan makes $6 per hour mowing lawns and $7.50 per hour bagging groceries. Last week, he
made a total of $129. The difference between the number of hours bagging groceries and
the number of hours mowing lawns was 10. How many hours did Ethan spend mowing lawns?
17. Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined
value of $8.85. How many of each type of coin does he have?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Topic 5: Linear Inequalities
Graph each linear inequality to show all possible solutions.
y
18. 2 x − 3 y < 6
19. x ≥ −3
y
x
x
Topic 6: Systems of Linear Inequalities
Graph each system of linear inequalities to show all possible solutions.
 y < 3x − 2
20. 
 y > −x + 3
y
2 x − y ≥ 0
21. 
3 x + y < 5
x
y
x
Topic 7: Systems of Linear Inequalities Application
22. Rob works part time at the Fallbrook Riding Stable. He makes $5 an hour exercising horses
and $10 an hour cleaning stalls. Because Rob is a full-time student, he can work no more than
12 hours per week. However, he must make at least $60 per week.
a. Write and graph a system of inequalities:
_________________________________
_________________________________
b. Write two possible solutions:
i. __________________________________
ii. __________________________________
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________
Unit 5: Systems of Equations & Inequalities
Date: _______________________ Bell: ______
Homework 11: Unit 5 Review
** This is a 2-page document! **
Solve each system of equations by graphing. Clearly give your solution.
2. -4x – 2y = -8
1. 3x + y = 5
y
y = 2x + 4
-x – y = 1
y
x
x
Solve each system of equations by substitution. Clearly give your solution.
3. 2x + 5y = -7
4. x – 3y = -24
7x + y = -8
5x + 8y = -5
Solve each system of equations by elimination. Clearly give your solution.
5. x + 2y = 3
6. 2x = 8y – 2
5x + 3y = 8
3x – 3y = 15
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
7. Karen and Holly took their families out to the movie theater. Karen bought three boxes of candy and
two small bags of popcorn and paid $18.35. Holly bought four boxes of candy and three small bags
of popcorn and paid $26.05. Find the cost for a box of candy.
8. Mr. Delaney broke his piggy bank with a sledge hammer and found that it only contained quarters
and pennies. If he had a total of 120 coins for a combined value of $16.32, how many pennies did he
have in his piggy bank?
Graph the following linear inequalities.
9. 2x – 4y < 8
10. y ≥ -3
y
y
x
x
Graph the following systems of linear inequalities.
11. y < 2x – 3
12. x – y ≥ 0
4x + 3y < 18
y > -x + 1
y
x
y
x
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
Name: _________________________________________
Date: _______________________________ Bell: ______
Algebra I Unit 5 Test
(Systems of Equations & Inequalities)
SHOW ALL WORK NEEDED TO ANSWER EACH QUESTION!
PLACE YOUR FINAL ANSWER IN THE BOX. GOOD LUCK! ☺
For questions 1 and 2, solve the system of equations by GRAPHING.
x + y = 4
1. 
2 x − 5 y = 15
y
y
 y = −2 x + 3
2. 
8 x + 4 y = 12
x
x
For questions 3 and 4, solve the system of equations by SUBSTITUTION.
6 x + 2 y = −26
3. 
 x − 6 y = 21
5 x + y = −10
4. 
 4 x − 7 y = −8
For questions 5-8, solve the system of equations by ELIMINATION.
 x + 2 y = −14
5. 
 x − y = 13
2 x − 3 y = 23
6. 
 x + 3 y = −20
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
2 x − y = 11
7. 
6 x − 3 y = 15
7 x = 3 y + 45
8. 
 4 x + 5 y = 19
For questions 9-11, define variables, set up a system, then solve by substitution or elimination.
9. Erin bought 4 jars of jelly and 6 jars of peanut butter for $19.32. Adam bought 3 jars of jelly and 5 jars
of peanut butter for $15.67. Find the cost of a jar of peanut butter.
10. Karen makes $5 per hour babysitting and $12 per hour giving music lessons. One weekend, she worked
a total of 18 hours and made $139. How many hours did she spend babysitting?
11. Carter has 37 coins, all nickels and dimes in his piggy bank. The value of the coins is $3.10. How
many dimes does Carter have?
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
12. Which graph represents the solution to the inequality 2x – y ≥ -3?
C.
B.
A.
13. Which inequality is shown on the graph?
D.
14. In the graph of y ≤ x, which quadrant is
completely shaded? Use the graph below to
determine.
A. x < 3
A. Quadrant I
B. x > 3
B. Quadrant II
C. y < 3
C. Quadrant III
D. y > 3
D. Quadrant IV
15. Which ordered pair is a solution to the linear inequality given below? Use the graph to determine.
y
3 x + 4 y ≥ 20
A. (-5, 1)
B. (0, -3)
x
C. (-4, -2)
D. (2, 7)
 y ≤ 2x + 1
16. Which graph represents the solution to the following system of inequalities? 
2 x − 5 y ≤ 10
A.
B.
C.
D.
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
17. Which ordered pair is NOT in the solution set to the following system of inequalities? Use the graph to
determine.
y
 3 x + y > −3

x + 2y < 4
A. (1, 1)
B. (-1, 2)
x
C. (4, -3)
D. (-5, 1)
18. In order to save money for prom this weekend, Tom is going to walk his neighbor’s dog for $6 per
hour and wash cars for $7.50 per hour. His mother told him he can work no more than 15 hours in
order to keep up with his homework. If Tom would like to make at least $75 to cover prom expenses,
help him determine combinations of hours he can work between these two jobs.
a. Write and graph a system of inequalities.
_________________________________
_________________________________
b. Write two possible solutions:
i. _________________________________
ii. _________________________________
BONUS: Solve the following system by substitution or elimination.
14
2
 3 x + y = 3

 4 x − 3 y = −10
 5
4
© Gina Wilson (All Things Algebra®, LLC), 2012-2016
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