810 Module 8 Study Guide
Solving Systems of Equations
Name:______________________ Period:__________
Vidal
Alcock
Feeney
1.) The school is selling tickets to the play. On the first day of ticket sales the school sold 1 adult ticket and 12
child tickets for a total of $60.60. The school took in $74.40 on the second day by selling 11 adult tickets and 6
child tickets. What is the price of one adult ticket and one child ticket?
Define your variables:
Set up your System and Solve:
The price of one adult ticket is __________. The cost of one child’s ticket is __________.
2.) Huong and Mark are selling cheesecakes for a school fundraiser. French silk cheesecakes cost $12 each and
chocolate marble cheesecakes cost $8 each. They sold a total of 15 cheesecakes and made a total of $160. How
many of each type of cheesecake did they sell?
Define your variables:
Set up your System and Solve:
They sold ___________ French silk cheesecakes and ___________ chocolate marble cheesecakes.
You are trying to decide if you should get a cable TV package or a subscription to WebPix.
Cable: You pay $100 for the installation and $50 per month for service.
WebPix: You would need to buy a new TV for $200 and then pay a $25 per month membership fee.
Let y be the cost of each plan
Let x be the number of months of service.
Write an equation for each plan.
Cable _____________________
WebPix _____________________
Graph the system.
y
700
600
Cost ($)
3.)
500
400
300
200
100
4
8
12
16
20
24
Months
After how many months are the total costs of the plans the same? __________________
When is Cable better? ______________________________________________________
When is WebPix better? ______________________________________________________
x
Solve the linear system by graphing.
1

y   x  5
4.) 
3

 y  3x  5
6-8: Sketch a graph for the following
situations and explain your reasoning.
6.) A system of two equations with only one
solution.
y
y
x
x
Explain:
Will the line through the points (0, -3) and
(-4, -3) intersect the following line?
5.) The line through the points (0 ,-2) and
(3, -3)
7.) A system of two equations with
no
y
solution.
y
x
x
Explain:
8.) A system of two equations with infinitely many solutions.
y
x
Explain:
Use substitution to solve the following:
𝑦 = −4𝑥 − 11
9.) {
−4𝑥 − 2𝑦 = 6
10.) {
4𝑥 + 7𝑦 = 13
𝑥 = 3𝑦 − 11
Use elimination to solve the following:
11.) {
5𝑥 − 6𝑦 = −17
−8𝑥 + 6𝑦 = 20
12.) {
7𝑥 − 8𝑦 = −4
−10𝑥 + 10𝑦 = 10
Answer the following for the system below:
−11𝑥 + 𝑦 = −22
13.) {
−16𝑥 − 2𝑦 = −32
a.) Describe the first step if you were to solve with elimination:
b.) Describe the first step if you were to solve with substitution: