Name: _________________________________
Date: __________________
Algebra 1 College Prep
Unit 2- Systems of Equations and Inequalities Test Review
Sections 6.1-6.3, 6.6
Solve each system by graphing.
1.
𝑦 = −3𝑥 + 3
𝑦 = 2𝑥 − 7
2.
𝑦 = −𝑥 + 6
𝑥 − 2𝑦 = 6
3.
4.
2𝑥 + 𝑦 = 6
𝑥 − 2𝑦 = 8
2𝑦 = 𝑥 − 14
𝑥+𝑦 =5
Solve each system by substitution OR elimination. .
5.
8𝑥 − 3𝑦 = −139
𝑥 = −𝑦 − 5
6.
−4𝑥 + 10𝑦 = −178
𝑦 = −10𝑥 + 3
7.
2𝑥 − 𝑦 = 12
3𝑦 = 𝑥 + 6
8.
7𝑥 + 𝑦 = 506
9𝑦 − 10 = 𝑥
9.
4𝑥  3𝑦 = 5
3𝑥  2𝑦 = 8
10.
𝑥  2𝑦 = 3
3𝑥  𝑦 = 2
11. Reasoning Without graphing, decide whether the following systems of linear equations has
one solution, infinitely many solutions, or no solution. Explain.
a. 8x = 2y – 16
y = 4x
b. y=3x+6
-3x+y=6
12. Writing Describe how to determine the solution of a system of two linear equations by graphing.
13. Reasoning If the graphs of two linear equations in a system do not intersect each other, what does that
tell you about the solution of the system? Explain.
14. Writing Explain the meaning of a solution to a system of equations.
Word Problem Practice
15. A cell phone provider offers a plan that costs $40 per month plus $.20 per text message sent or
received. A comparable plan costs $60 per month but offers unlimited messaging. Write a system of
equations to help you answer the following questions.
a. How many text messages would you have to send or receive in order for the plans to COST THE
SAME each month?
b. If you send or receive an average of 50 text messages each month, which plan would you choose?
Why?
16. The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day,
2200 people enter the fair and $5050 is collected. How many children and how many adults
attended?
17. There are 785 students in the senior class. If there are 77 more females in the class than males, how
many male and female seniors are there in the class?
18. Your math test has 38 questions and is worth 200 points. The test consists of multiplechoice questions worth 4 points each and open-ended questions worth 20 points each. How
many of each type of question are there?
19. Mark is a student, and he can work for at most 20 hours a week.
He needs to earn at least $90 to cover his weekly expenses. His
dog-walking job pays $5 per hour and his job as a car wash attendant pays $4 per hour.
Let x=number of hours of worked walking dogs and y=number of hours as a car wash attendant.
a. Write a system of inequalities to model the situation, and graph the inequalities. Label your axes‼
y
x
b. Which pairs (x, y) of represent hours that Mark could work to meet the given conditions? Select ALL
that apply!
A. (19, 1)
B. (5, 14)
C. (10, 10)
D. (7, 9)
20. A friend makes $15 per hour waiting tables and $11 per hour mowing lawns. His
goal is to make at least $700 per week. He does not want to work any more than 55
hours in a week.
a. Write a system of inequalities for the given situation and graph the inequalities. Label
your axes‼
y
x
b. Given the conditions from Part A, your friend prefers mowing lawns over waiting tables. What is the
maximum number of hours he can mow lawns and be able to earn at least $700 per week? (NOTE: He
can still work at BOTH jobs to earn $700).
What is a system of inequalities that is represented by the graph below?
21.
y
x
22.
y
x
Graph the following system of linear inequalities.
23.
24.
𝑦  2𝑥  1
𝑦  3𝑥 + 4
𝑦  𝑥 + 3
3𝑥 + 3𝑦  9
25.
26.
𝑥 + 𝑦  3
2𝑥 + 2𝑦  2
𝑦 ≤ −𝑥 + 6
3
𝑦 > 𝑥−4
2