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Review Systems of Linear Equations and Inequalities - Printable Math Worksheets 8th - 12th Grade - Wayground

Review Systems of Linear Equations and Inequalities

Rhea Hartman

Created by Rhea Hartman

16 questions

8th - 12th Grade

Math

Updated Apr 2026

Review Systems of Linear Equations and Inequalities is a 16-item mathematics worksheet for students in Grades 8–12. It combines 15 multiple-choice questions with one open-ended task to review how to identify solutions from graphs, determine whether a system has one, no, or infinitely many solutions, and select graphs or ordered pairs that satisfy systems. Students also translate real-world situations into systems of equations and interpret graphs of linear inequalities, including solution regions. The open-ended problem asks students to write and solve a system modeling two students’ hourly earnings, giving them practice connecting equations to a multi-step context. Multiple-choice items reinforce graph interpretation, equation selection, solution checking, and inequality shading. This free printable worksheet includes a complete answer key, making it useful for independent review, guided practice, homework, or an assessment of students’ readiness with systems of equations and inequalities.

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Review Systems of Linear Equations and Inequalities

Total questions: 16

Name
Class
Date
1.

On a graph, the solution to a system of linear equations is given by _____.

a)

The x-intercept of each line

b)

The y-intercept of each line

c)

All points on either line

d)

The point of intersection of the lines

2.
Look at the graph to the left. Which of the following ordered pairs represents the solution to the system?

Look at the graph to the left.

 

Which of the following ordered pairs represents the solution to the system?

a)

(1, 2)

b)

(2, 2)

c)

(2, 1)

d)

(0, 2)

3.

Look at the system of equations below:

y=ax+cy=ax+c  

y=bx+dy=bx+d  

For the system to have no solution, what must be true of aa and bb ?

a)

a+b=ca+b=c  

b)

a=ba=b  

c)

a>ba>b  

d)

a<ba<b  

4.

Which graph represents the following system of equations?

y=2x+2y=2x+2  

y=4x+4y=4x+4  

a)
Which graph represents the following system of equations?
b)
Which graph represents the following system of equations?
c)
Which graph represents the following system of equations?
d)
Which graph represents the following system of equations?
5.

2x+3y=12x+3y=1  

−4x−2y=−6-4x-2y=-6  

Which of the following ordered pairs represents the solution to the system?

a)

(-1, 1)

b)

(1, -1)

c)

(2, -1)

d)

(1, 1)

6.

Vans charges $140 per pair of shoes and Nike charges $135 per pair of shoes plus $20 for shipping and handling. Which system of equations could be used to answer the question, "For what number of shoes do both companies charge the same price?"

a)

y = 140

y = 135 + 20x

b)

y = 140

y = 135x + 20

c)

y = 140x

y = 135x + 20

d)

y = 140x

y = 135 + 20x

7.
Jack's work is shown on the left. What can be concluded about the solution to the system based on Jack's work?

Jack's work is shown on the left. What can be concluded about the solution to the system based on Jack's work?

a)

Jack made a mistake

b)

There is no solution to the system

c)

There are infinitely many solutions to the system

d)

There is one solution to the system

8.

For its winter fundraiser the senior class is selling wreaths and flower arrangements. Each wreath sells for $20 and each arrangement sells for $15. Sarah sold 12 items and raised $220.

 

         How many wreaths did Sarah sell?

a)

4

b)

6

c)

8

d)

10

9.

State the number of solutions to the system:

2y=−6x+82y=-6x+8  

3x+y=43x+y=4  

a)

No solutions

b)

1 solution

c)

2 solutions

d)

Infinitely many solutions

10.

Michelle and Julie are 17-year old twins, who decided to save their earnings to buy a car.  One week Michelle worked 8 hours and Julie worked 14 hours, and they saved $128.  The next week Michelle worked 12 hours, Julie worked 16 hours, and they earned $162. Write a system of equations to model the situation. Solve the system to determine how much each girl earns per hour.

4 lines
11.

y>−x+2y>-x+2  

y>23x−13y>\frac{2}{3}x-\frac{1}{3}  

Which of the following is a graph of the system above?

a)
-x+2"> \frac{2}{3}x-\frac{1}{3}"> Which of the following is a graph of the system above?
b)
-x+2"> \frac{2}{3}x-\frac{1}{3}"> Which of the following is a graph of the system above?
c)
-x+2"> \frac{2}{3}x-\frac{1}{3}"> Which of the following is a graph of the system above?
d)

none of these

12.
Which is not a solution to the system shown in the graph?

Which is not a solution to the system shown in the graph?

a)

(-1, 1)

b)

(0, 1)

c)

(-1, -1)

d)

(1, -1)

13.

y>−2x+2y>-2x+2  

y≤x+3y\le x+3  

Which of the following points is a solution to the system?

a)

(-6, 2)

b)

(4, 1)

c)

(2, -4)

d)

(-1, 6)

14.
Which system of linear inequalities is shown in the graph?

Which system of linear inequalities is shown in the graph?

a)

x<−4x<-4  

y>2y>2  

b)

x≥−4x\ge-4  

y≤2y\le2

c)

x>−4x>-4  

y<2y<2

d)

x<2x<2  

y>−4y>-4

15.
Which is the solution region for the system of inequalities?

y<−2x+3y<-2x+3  

y≥12x−2y\ge\frac{1}{2}x-2  

Which is the solution region for the system of inequalities?

a)

Region A

b)

Region B

c)

Region C

d)

Region D

16.
Which system of inequalities is shown in the graph?

Which system of inequalities is shown in the graph?

a)

y≥−x+2y\ge-x+2  

y<32x−2y<\frac{3}{2}x-2  

b)

y>−x+2y>-x+2  

y≤32x−2y\le\frac{3}{2}x-2  

c)

y≤−x+2y\le-x+2  

y>32x−2y>\frac{3}{2}x-2  

d)

y<−x+2y<-x+2  

y≥32x−2y\ge\frac{3}{2}x-2  

WaygroundAnswer Key

Review Systems of Linear Equations and Inequalities

Total questions: 16

1.
d)

The point of intersection of the lines

2.
c)

(2, 1)

3.
b)

a=ba=b  

4.
b)
5.
c)

(2, -1)

6.
c)

y = 140x

y = 135x + 20

7.
b)

There is no solution to the system

8.
c)

8

9.
d)

Infinitely many solutions

10.
n/a
11.
c)
12.
c)

(-1, -1)

13.
b)

(4, 1)

14.
c)

x>−4x>-4  

y<2y<2

15.
a)

Region A

16.
b)

y>−x+2y>-x+2  

y≤32x−2y\le\frac{3}{2}x-2  

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FAQs

What does this worksheet cover?

This worksheet reviews systems of linear equations and inequalities through 15 multiple-choice questions and one open-ended modeling problem. Students identify graph intersections, determine whether systems have one, no, or infinitely many solutions, test ordered pairs, choose matching graphs and inequality regions, and write and solve a system from an hourly-earnings scenario. These varied formats build the ability to connect algebraic representations, graphs, and real-world situations.

How can I use this worksheet to teach systems of linear equations and inequalities?

Use the early graph and ordered-pair questions to introduce a system’s solution as the point shared by both equations, then discuss how parallel and coincident lines represent no solution or infinitely many solutions. Move next to the pricing and fundraiser problems so students translate quantities and costs into equations before solving. Finish with the open-ended earnings task and the inequality-graph items, asking students to explain how boundary lines and shaded regions show the solution set.

What mistakes should I watch for when students complete this worksheet?

Students may confuse an x- or y-intercept with the ordered-pair intersection that solves both equations, or select a point that lies on only one line. In the word problems, watch for reversed coefficients, omitted shipping costs, and assigning the wrong variable to each quantity. For the inequality items, students may choose the correct boundary lines but shade the wrong region, or misread a graph when deciding whether a point is a solution.

How do I assign and grade this worksheet?

This systems of equations and inequalities worksheet is available as a printable PDF and as a digital quiz on Wayground. It includes a complete answer key for the multiple-choice items and the open-ended modeling task, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the equations, graph questions, and word-problem text easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while preserving its systems-of-equations and inequalities practice.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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