Algebra 1B: Unit 1 Reteach
Watch the recording for the Unit 1 reteach (press CTRL and the link) and complete this review as you watch.
When you finish the review, you may answer the retest questions at the end. The retest will not be graded
unless all of the review is completed. Once you complete this whole document, webmail it to me.
Solving Systems by Graphing

Ex:
Easiest to do when we have both equations solved for y.
y = 3x + 4
−3
𝑦= 𝑥−7
4
Solution is where the lines intersect.
How to find the intersection point on a calculator:
TRACE
2nd
#5
ENTER (3X)
You Try: (put in your graphing calculator)
y = 3x - 2
−1
𝑦= 𝑥+5
Solution: (2.15, 4.46)
4
Solving Systems by Substitution

This is best done when one of the equations is already solved for a variable.
3𝑥 + 2𝑦 = 23
1
𝑥−4=𝑦
2
EX:
You Try:
y=8–x
7 = 2x – y
Show the work here:
Show the work here:
Show the work here:
Show the work here:
3x+2t=23
3x+2y=23
7=2x-y
7=2x-y
3x+2(1/2x*4)=23
3(7.75)+2y=23
7=2x-(8-x)
7=2(5)-y
3x+1x-8=23
23.25+2y=23
7=2x-8+ x
7=10-y
-23.25
7=3x-8
-10 -10
2y/2=-0.25/25
+8 +8
-3=-y
y=0.125
15/3=3x/3
y=-3
4x-8=23
+8 +8
4x/4=31/4
x=7.75
-23.25
x=5
Solution:
Solution:
(7.75,-0.125)
(5,-3)
Solving Systems by Elimination

Ex:
This method is easier when 2 equations can be put in order or you can add or subtract the equations so that one
of the variables will be eliminated.
3x + 4y = 17
3x – 4y = -29
Show the work here:
Show the work here:
3x+4y=17
3x+4y=17
3x-4y=-29
3(-2)+4y=17
6x/6 =-12/6
-6+4y=17
x=-2
+6
*A little bit harder example:
+6
4y/4==23/4
Solution:
y=5.75
(-2, 5.75)
2x – 7y = 9
4x + 4y = 3
Show the work here:
Show the work here:
2x-7y=9
2x-7y=9
*-2 -4x+14y=-18
2x-7(-5/6)=9
4x+4y=3
*-2 4x+4y=3
2x+5.83=9
Solution:
(1.583,-5/6)
18y/18=-15/18
-5.83 -5.83
Y=-5/6
2x/2=3.167/2
*A
little bit harder still example:
X=1.583
3x – 4y = 9
2x – 3y = 17
Show the work here:
Show the work here:
3x-4y=9
3x-4=9 *2 6x-8y=18
3x-4(-33)=9
2x-3y=17 *-3 -6x+9y=-51
3x+132=9
Solution:
1y/1=-51/1
-132 -132
Y=-33
3x/3=-123/3
*Be sure to find the y value yourself.
X=-41
*Be sure
to solution
find the of
y value
yourself.
What
is the
this system?
Solution: (5,6)
Graphing Inequalities
When to use a
Dotted line
< or >
Y=mx+b
Solid line
≤ or ≥
(-41,-33)
EX:
𝑦 ≥ −3𝑥 − 2
𝑦 ≤𝑥−8
One more inequality system
𝑦 > −5
𝑦 ≤ 3𝑥 + 4
EX: (Using your calculator)
𝑦 ≥ 4𝑥 − 3
𝑦 ≤ −3𝑥 + 4
Which part of the graph will be the solution area?
4
Number of Solutions
How can you determine if a pair of equations has:
1 solution
The intersect
No solution
They don’t intersect
An infinite number of solutions
They become the same line
Word Problem
Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost $228. Write and
solve a system of equations to find how many children and how many adults were in this group.
Let a =
Let c =
Equations:
Solution:
A+c=11
2children,9 adults
22a+15c=228
Show work here:
A=c=11
*-22
-22a+-22c=-242
*22a+15c= 228
-7c/7=-14/7
C=2
UNIT 1B RETEST
Answer each of the questions below by placing your answer in the blank on the left. Please remember…. The retest will not be
graded unless all of the reteach is completed above. The highest grade you can earn on a retest is 70.
1. B.
Anna burned 15 calories per minute running for x minutes and 10 calories per
minute hiking for y minutes. She spent a total of 60 minutes running and hiking
and burned 700 calories. The system of equations shown below can be used
to determine how much time Anna spent on each exercise.
15x + 10y = 700
x + y = 60
What is the value of x, the minutes Anna spent running?
A 10
B 20
C 30
D 40
What is the solution for the two algebraic equations below?
2. A.
3x - 2y = 25
5y = 2x – 24
A (7, -2)
B (-2, 7)
C (17, 2)
D (1, -11)
What is the solution to the system of equations below?
3. A.
3𝑥 + 2𝑦 = 6
3𝑥 + 6𝑦 = 18
A.
(0, 3)
B. (0, 6)
C. (1, 2)
D. (3, 0)
Which ordered pair is the solution to the system of equations below?
4. D.
𝑥 + 3𝑦 = 7
𝑥 + 2𝑦 = 10
A. (7/2, 13/4)
B. (7/2, 17/5)
C. (-2, 3)
D. (16, -3)
5.
𝑥 + 3𝑦 = 7
𝑥 + 2𝑦 = 10
What is the solution of the system of equations shown above?
A. (1, -2)
B. (1, 2)
C. (5, 10)
D. (-5, -10)
6.
Which graph best represents the solution to this system of inequalities?
2𝑥 > 𝑦 − 1
2𝑥 − 5𝑦 ≤ 10
What ordered pair is the solution to the system of equations graphed below?
7.
A (0, -2)
B (-4, 0)
C (2, 6)
D (1, 2)
Equations 3 = y + x and y = 2x - 3 are graphed below.
8.
Which ordered pair is the solution of this system
of equations?
A (1, 2)
B (3, 0)
C (2, 1)
D (0, 3)
9.
There are 9 books stacked on a shelf. The thickness of each book is either 1 inch or 2
inches. The height of the stack of 9 books is 14 inches. Which system of equations can
be used to determine x, the number of 1-inch-thick books in the stack, and y, the
number of 2-inch-thick books?
A) x + y = 14
2x + y = 9
10.
B) x + y = 14
x + 2y = 9
D) x + y = 9
2x + y = 14
Sam purchased two bottles of water and three hot dogs at the ballpark for $8.50. Mary
purchased one bottle of water and two hot dogs for $5.25. What system of equations
could be solved to determine the prices in dollars of a hot dog (h) and a bottle of water
(w)?
A) 2w + 3h = 8.50
w + 2h = 5.25
11.
C) x + y = 9
x + 2y = 14
B) 3w + 2h = 8.50
w + 2h = 5.25
C) w + h = 8.50
w + h = 5.25
D) 3w + 2h = 8.50
2w + h = 5.25
The graph for the system of inequalities without the shading of its solution set is shown
on the coordinate grid.
2x + y < 1
Which area should be shaded to represent the
3x - y < -5
solution set of this system of inequalities?
A) Area 1
B) Area 2
C) Area 3
D) Area 4
12.
Greg is going to solve the system of linear equations below.
13.
First Equation: 8x - 2y = 8
Second Equation: 3x + 3y = 9
Which of the following would Greg NOT use to solve this system of equations?
A) Solve the second equation for y and then substitute the result into the first equation.
B) Multiply the first and second equation by -6 to eliminate the y variable.
C) Solve the first equation for y and then substitute the result into the second equation.
D) Multiply the first equation by 3 and the second equation by 2 to eliminate the y
variable.
What system of inequalities best represents the graph shown below?
14.
A) y > -2 and y > x + 1
B) y > -2 and y < x + 1
C) y < -2 and y > x + 1
D) y < -2 and y < x + 1