Unit 7: System of
Equations
Homework Packet
Name: ______________________
Class Period: _________________
Teacher: ____________________
1
Graphing and Slope-Intercept Review
Graph the following points.
1. L(–2, 0)
2. M(5, 2)
3. N(–4, –3)
4. P(1, –1)
5. Q(0, –4)
6. R(3, –3)
State the slope and y-intercept of each line.
7. y = 2x + 4
8. y = 1/2x – 6
9. y = -5x
10. y = -3/4x + 2
Translate each equation into slope-intercept form. Then, state the slope and y-intercept.
11. 4y = 2x + 20
12. 6x – 3y = 12
2
Graphing Linear Equations Review
Graph each of the following on the graph provided.
1. y = 2x - 3
2. y = -3x + 2
3. 6x + 24 = -12y
4. 2x - y = 4
3
Introduction to Systems of Equations
For each problem determine which ordered pair is a solution to the system of equations. SHOW ALL
YOUR WORK to justify your answer.
Example 1
Determine which of the points (1, 3), (0, 2) or (2, 7) is a solution to the following system of equations.
y = 4x – 1
y = 2x + 3
Example 2
What is the solution of the system of equations?
y=x–4
y = –3x
Example 3
What is the solution of the system of equations?
y = x – 10
y = 2x + 5
4
Solve Systems by Graphing – Day 1
Graph the equations. You MUST check your answer completely. No check, no credit!
1)
y  3x  1
y  2 x  4
3)
2)
3
x2
4
3
y  x 1
2
y
2 x  6 y  12
2x  4 y  8
Remember to put the
equation into the slopeintercept form before
graphing.
5
Solve Systems by Graphing – Day 2
1. Your school is donating items to the local food pantry. Your homeroom is having a competition to see who will donate
the most items. You have already donated 14 items and plan to donate 3 more each week. Your friend has already
collected 8 items and plans to collect 5 more items each week. How many weeks will it take for both of you to have
collected the same amount? How much will each of you have collected at that time?
a) Define the variable(s)
b) Write a system of equations for the situation.
First equation __________________
Second equation __________________
c) GRAPH each equation to determine when you will both have collected the same amount.
Answer
2. The seventh grade class supplied bags of snacks and beverages for the school dance. They supplied 50 more
beverages than bags of snacks. The dance was supplied with a total of 400 items. How many of each were
supplied.
a) Define the variable(s)
b) Write a system of equations for the situation.
First equation __________________
c) Graph the system.
Second equation __________________
Answer:
6
Solve Systems by Substitution – Day 1
Solve each system by substitution. Write your answer as an ordered pair.
1. y = 7x – 10
y = -3
2. y = -8
y = -2x – 12
3. y = 6x
y = 5x + 7
4. y = 6x – 14
y = -8x
5. y = 2x – 15
y = 5x
6. 6x + 7y = 20
y = 2x
7
Solve Systems by Substitution – Day 2
Solve each system using substitution
1) 4x + 7y = 19
y=x+9
2) y = 6x + 11
2y – 4x = 14
3) 2x – 8y = 6
y = -7 – x
4) x = 2y – 1
3x – 2y = -3
5) y + x = 3
3y + x = 5
6) 2x – 3y = -4
x - 7= - 3y
8
Graphing and Substitution Quiz Review
Solve each system of equations by graphing.
1. y = x + 4
y = –2x – 2
2. y = 5x – 1
y = 2x + 2
3. y = x – 1
y - 2x = 3
4. y = 6x – 3
y+3=
Julie has 81 pieces of jewelry. She has twice as many earrings as she has necklaces. How many of each does
Julie have? a) Write a system of equations for the situation (2 separate equations). b) Find the solution.
5.
a) Write a system of equations.
Equation #1 ___________________
Equation #2 ___________________
b) Find the solution.
Answer the question:
9
Use substitution to solve each system of equations.
6. y = 4x
x+y=5
7. y = 2x
x + 3y = –14
8. y = 3x
2x + y = 15
9. x = –4y
3x + 2y = 20
10.
y=x–1
x+y=3
12. y = 4x – 1
y = 2x – 5
11. x = y – 7
x + 8y = 2
13. y = 3x + 8
5x + 2y = 5
14. Is (3,6) a solution to this system of equations? Show your work!
2x + 11y = 70
5x + 2y = 20
10
Solving Systems by Elimination – Day 1
1) - 2x + 3y = 40
2x + 5y = 24
2) 3x + 4y = 19
-3x – 6y = 33
3) - 2x - 2y = 6
2x + 5y = - 27
4) 2x – 3y = 9
-5x + 3y = 30
5) - 5x - y = - 52
5x - 5y = - 80
6) x - 3y = - 20
-x - 5y = - 40
11
Solving Systems by Elimination – Day 2
Use elimination to solve each system of equations.
1.
3.
5.
7.
2 x  5y  3
 x  3 y  7
7 x  4 y  4
5x  8 y  28
2x  y  0
5x  3 y  2
7 x  3 y  25
 2 x  y  8
2.
4.
6.
8.
2x  y  3
4 x  4 y  8
4 x  2 y  14
3 x  y  8
3 x  2 y  10
9 x  6 y   6
4 x  3 y  11
3x  5 y  11
12
Solve Special Types of Systems
Solve each System by Graphing.
3
x2
4
3
y  x4
4
1) y 
2)
y
1
x2
2
6 y  3 x  12
Solve each System by Elimination.
3) 2x + 4y = 6
x + 2y = 5
4) 3m + 6n = 18
m + 2n = 6
Solve each System by Substitution.
5) 4x - 8y = 6
x = 2y
6) 4x – 3y = 20
x = 2y
13
Elimination and Special Types Quiz Review
Use the elimination (linear combinations) method to solve the following linear systems:
1.
x+y=9
x–y=7
2.
3.
4.
1._____________
x – 2y = 8
-x + 3y = -5
2.______________
2x – 3y = -16
x + 3y = 10
3.________________
-5x + 3y = 15
6x – 2y = -18
4.________________
14
5.
6.
4x – 5y = -18
5x + 4y = -2
5._______________
6x + 9 y = 12
2x + 3y = 4
6._______________
7. x  y  3
2x  2 y  4
8.
7._____________
x y 3
y  1x  3
8._____________
15
Solving Systems of Equations Word Problems – Day 1
1. Michelle Is making goodie bags for Christmas filled with chocolates and hard candies. Chocolates cost
$2.50 per lb. and hard candies cost $3.00 per lb. Michelle bought a total of 15 lbs. and spent a total of $40. How
many lbs. of each type did Michelle purchase?
a) Define your variables.
b) Write an equation showing that Michelle spent a total of $40 on chocolates and hard candies.
c) Write an equation showing that Michelle bought a total of 15 lbs. of chocolates and hard candy.
d)
Solve the system of equations to find out how many lbs. of chocolates and how many lbs. of hard
candies Michelle bought.
Chocolates = ________
Hard Candies = _________
2. 20,000 tickets were sold to the Green Day concert. Stage level seats cost $105 and higher level seats cost
$75. If the total money collected from selling tickets was $1,740,000, how many tickets of each type were sold?
a) Define your variables.
b) Write an equation showing that 20,000 tickets were sold.
c) Write an equation showing $1,740,000 was collected
d) Solve the system of equations to find out how many of each type of ticket was sold.
State level seats = ________
Higher Level seats = _________
16
Solving Systems of Equations Word Problems – Day 2
1. Tyler is catering a banquet for 250 people. Each person will be served either a chicken dish that costs $5 each
of a beef dish that costs $7 each. Tyler spent $1500 total on the banquet. How many dishes of each type did
Tyler serve?
Chicken Dishes = ________
Beef Dishes = _________
2. Your teacher is giving a test worth 100 points. The test contains a total of 40 questions. Some questions are
worth 2 points and some questions are worth 4 points on the test. How many of each type of question are on the
test?
2 point problems = ________
4 point problems = _________
17
Systems of Equations Study Guide
Graph the system to find the solution: Be sure all equations are in slope intercept form BEFORE you
graph.
 y  2x  3

1. 
1
 y   2 x  2
 y  x  2
2. 
3x  y  2
 y  2x  5
3. 
 y  2 x  1
3

y  x  4
4. 
2
2 y  3x  8
5. Is the point (2, 1) a solution to the system?
y = 6x – 11
-2x – 3y = -7
6. Select the coordinate point that is a solution to the system.
a) (-3, -4)
b) (3, 4)
c) (3, -4)
-7x – 2y = -13
x – 2y = 11
d) (-3, 4)
18
Solve by using the substitution method. Show your work!
7. y = x + 2
8. 6x – 5y = 22
y = 3x + 4
y = -8
9. 2y = 4x + 6
y = 2x + 3
Solve by the elimination method. Show your work!
10. 2x + y = 3
3x – y = 2
11. 5x + y = 9
10x – 7y = -18
12. -7x + y = -19
-2x + 3y = -19
Solve using the method of your choice. Hint: Remember the format of the problem helps determine which
method to use. Show your work!
15. 2x + y = 20
6x – 5y = 12
16. y = 2x - 5
y = 3x + 4
17. 4y = 2x - 36
y = 5x
19
Solve each systems word problem by setting up two equations and solving. Show your work!
18. A store sells two different kinds of rulers, plastic and wood. The receipts show that they have sold 35 total
rulers today. The plastic rulers cost $2 each and the wood rulers cost $3 each. $82 worth of rulers were sold
today. How many of each type of ruler were sold?
19. Isaiah bought a total of 22 pieces of candy. The tootsie rolls cost 3 cents each and the jolly ranchers cost 5
cents each. If Isaiah spent a total of $90 cents, how many of each candy did he purchase?
20. The sum of two numbers is 17 and their difference is 29. What are the two numbers?