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Systems of equations and inequalities - Printable Math Worksheets 9th Grade - Wayground

Systems of equations and inequalities

Kate Abernathie

Created by Kate Abernathie

15 questions

9th Grade

Math

Updated Sep 2026

Systems of equations and inequalities is a Grade 9 mathematics worksheet with 15 multiple-choice questions. Students solve pairs of linear equations, identify ordered-pair solutions, recognize when a system has no solution, and determine which points satisfy two inequalities. The worksheet also builds graphing and interpretation skills: students identify shaded regions, read systems of inequalities from graphs, test whether points satisfy individual inequalities, and locate points in overlapping solution regions. It is useful for guided practice, independent review, or a formative check after instruction on systems of equations and graphing inequalities. This free printable worksheet includes a complete answer key for efficient teacher review and grading.

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Systems of equations and inequalities

Total questions: 15

Name
Class
Date
1.
What is the solution?
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
2.
The solution to this system is...
The solution to this system is...
a)
(4, -2)
b)
(4, 2)
c)
(-2, 4) 
d)
(-4, -2)
3.
Solve the system of equations
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
4.
Solve the system of equations
y = 5x + 1
y = 3x + 13
a)
(6, 31)
b)
(31, 6)
c)
(4, 21)
d)
(2, 11)
5.
Which of the following points is a solution to the system of equations below?
x + 2y ≥ 4
3x − 2y < 4
Take your time!
a)
(0, 0)
b)
(2, 1)
c)
(2, 2)
d)
(-1, 1)
6.
Given the system, determine a solution.
Given the system, determine a solution.
a)
No solution
b)
Infinite solutions
c)
(-5, 5)
d)
(5, -5)
7.
Given the following systems of inequalities, which region should be shaded?

Given the following systems of inequalities, which region should be shaded?

a)

1

b)

2

c)

3

d)

4

8.
Which system of inequalities is shown?
Which system of inequalities is shown?
a)
y ≥ -x - 1
y < x + 4
b)
y < -x - 1
 y ≥ x + 4
c)
y > -x - 1
y ≥ x + 4
d)
y > -x - 1
y ≥ x + 3
9.
Tell whether the ordered pair 
(-3, 0) is a solution of the given system.
y ≤ x + 4
y ≥ 2x - 6
a)
Yes
b)
No
10.
Solve the system of inequalities by graphing.

Solve the system of inequalities by graphing.

a)
Solve the system of inequalities by graphing.
b)
Solve the system of inequalities by graphing.
c)
Solve the system of inequalities by graphing.
d)
Solve the system of inequalities by graphing.
11.
Which point is a solution?

Which point is a solution?

a)

(0, 6)

b)

(-3, 5)

c)

(1, 0)

d)

(-4, 3)

12.
Is (-2, 0) a solution to the system?

Is (-2, 0) a solution to the system?

a)

Solution

b)

Not a solution

13.
Which point is in the overlap of the shaded regions?

Which point is in the overlap of the shaded regions?

a)

(8,-5)

b)

(20,5)

c)

(9,10)

d)

(-7,1)

14.
Which point is a solution to both inequalities?

Which point is a solution to both inequalities?

a)

(-10,-5)

b)

(-20,25)

c)

(40,30)

d)

(40,-10)

15.
Which point is part of the solution ?

Which point is part of the solution?

a)

(4,0)

b)

(0,4)

c)

(10,5)

d)

(5,10)

WaygroundAnswer Key

Systems of equations and inequalities

Total questions: 15

1.
a) (6, 3)
2.
a) (4, -2)
3.
a) (1,3)
4.
a) (6, 31)
5.
c) (2, 2)
6.
a) No solution
7.
a)

1

8.
c) y > -x - 1
y ≥ x + 4
9.
a) Yes
10.
b)
11.
c)

(1, 0)

12.
b)

Not a solution

13.
d)

(-7,1)

14.
c)

(40,30)

15.
d)

(5,10)

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FAQs

What does this systems of equations and inequalities worksheet help Grade 9 students practice?

This 15-question multiple-choice worksheet helps students solve systems of linear equations, identify ordered-pair solutions, and recognize a system with no solution. It also asks students to test points in systems of inequalities, identify shaded regions and graphed systems, and find points in the overlap of solution regions.

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

Use the equation items first to review how students find an ordered pair that satisfies both equations, then discuss how substituting the pair into each equation confirms the solution. For the inequality items, have students check boundary symbols, test a point in each inequality, and explain why the overlapping shaded region represents solutions to both conditions.

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

Students may reverse the coordinates in an ordered pair, verify a point in only one equation or inequality, or select a point that satisfies one condition but not both. In the graphing questions, watch for confusion between < and ≤ or between > and ≥, as well as errors identifying the overlap of two shaded regions.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the multiple-choice prompts, coordinate pairs, and inequality notation easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when appropriate.

Where can I find more worksheets like this on Wayground?

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

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