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System of Linear Equations and Inequalities and Exponents - Printable Math Worksheets 9th Grade - Wayground

System of Linear Equations and Inequalities and Exponents

Kristine Joy Torela

Created by Kristine Joy Torela

22 questions

9th Grade

Math

Updated Oct 2026

This Grade 9 mathematics worksheet gives students 22 multiple-choice opportunities to work with systems of linear equations and inequalities. Students interpret graphed boundary lines, select inequalities that match shaded regions, test ordered pairs in a system, identify points that do or do not satisfy both inequalities, and connect systems to their graphical solution sets. The worksheet also includes solving systems of equations, including elimination, determining a missing coordinate, and recognizing when a system has no solution or infinitely many solutions. Use this free printable worksheet to check whether students can move between equations, graphs, ordered pairs, and solution descriptions. Its varied question format helps reveal whether an error comes from reading a boundary symbol, testing a point, interpreting an intersection, or carrying out algebraic elimination. It is designed for Grade 9 math practice, review, or assessment and includes a complete answer key for efficient checking.

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WaygroundWorksheets

System of Linear Equations and Inequalities and Exponents

Total questions: 22

Name
Class
Date
1.
Which of the following equations match the given graph?
Which of the following equations match the given graph?
a)
y ≤ -3/4 x + 3
b)
y ≥ -3/4 x + 3
c)
y < -3/4 x + 3
d)
y > -3/4 x + 3
2.
Which of the following equations match the given graph?
Which of the following equations match the given graph?
a)
y ≥ 2/5x + 1
b)
y ≥ -2/5x + 1
c)
y≤  2/5x + 1
d)
y ≥ -2/5x - 1
3.
Is (-2,4) a solution to the system?
Is (-2,4) a solution to the system?
a)
Solution
b)
Not a solution
4.
Match the system to the graph (solution set is on the left)
Match the system to the graph (solution set is on the left)
a)
y ≤ 3x   and  y ≤ -2x + 4
b)
y > 3x   and  y > -2x + 4
c)
y < 3x   and  y > -2x + 3
d)
y > 3x   and  y < -2x + 4
5.
Which of the following is not a solution to this system of inequalities?
Which of the following is not a solution to this system of inequalities?
a)
(0,-1)
b)
(0,3)
c)
(4,0)
d)
(6,-2)
6.
Which system of inequalities matches the graph?
Which system of inequalities matches the graph?
a)
y > 2x - 4
y < 2
b)
y < 2x - 4
y < 2
c)
y > 2x - 4
y <  2 
d)
y < 2x - 4
y <   -2
7.
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.
8.
Which of the following is a solution to the systems of inequalities?

Which of the following is a solution to the systems of inequalities?

a)

(0, 0)

b)

(-3, 0)

c)

(2, -5)

d)

(3, -1)

9.
Which of the following is a solution to the systems of inequalities?

Which of the following is a solution to the systems of inequalities?

a)

(0, -2)

b)

(-3, 0)

c)

(-3, 2)

d)

(1, 1)

10.
How many solutions will this system have?
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
11.

What is the value of the y-coordinate in this system of linear equations?

6x + 10y = -32 and 6x + 9y = -27

a)

y = 5

b)

y = 0

c)

y = -5

d)

y = 1

12.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
13.
What is the solution to the system?
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
14.

Solve the system of equations using elimination

3x+7y=−23x+7y=-2  

4x−7y=−194x-7y=-19  

a)

(1, −3)\left(1,\ -3\right)  

b)

(2.4, −1.3)\left(2.4,\ -1.3\right)  

c)

(−3,  1)\left(-3,\ \ 1\right)  

d)

(−1.3, 2.4)\left(-1.3,\ 2.4\right)  

15.
What is the solution to the system?
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution 
d)
(6, -2)
16.
If the solution is infinitely many the lines will ________?
a)
intersect at exactly one point
b)
be parallel
c)
overlap each other
d)
never exist
17.
Rewrite the expression using a radical exponent:

Rewrite the expression using a radical exponent:

a)

x34x^{\frac{3}{4}}

b)

x43x^{\frac{4}{3}}

c)

x13x^{\frac{1}{3}}

d)

x14x^{\frac{1}{4}}

18.
Rewrite the expression using a radical exponent:

Rewrite the expression using a radical exponent:

a)

x35x^{\frac{3}{5}}

b)

x15x^{\frac{1}{5}}

c)

x8x^8

d)

x2x^2

19.
Rewrite the radical exponent:

Rewrite the radical exponent:

a)

 5x\ ^5\sqrt{x}

b)

 1x5\ ^1\sqrt{x^5}  

c)

  6x\ ^{\ 6}\sqrt{x}  

20.
What is the equation for the table?
What is the equation for the table?
a)
y = 4(2)x
b)
y = 2(4)x
c)
y = 2(8)x
d)
y = -2(4)x
21.
Is the pictured graph growth, decay, or linear or none?
Is the pictured graph growth, decay, or linear or none?  
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
22.
Is this exponential growth or decay?
Is this exponential growth or decay?
a)
Growth
b)
Decay
WaygroundAnswer Key

System of Linear Equations and Inequalities and Exponents

Total questions: 22

1.
b) y ≥ -3/4 x + 3
2.
c) y≤  2/5x + 1
3.
a) Solution
4.
d) y > 3x   and  y < -2x + 4
5.
a) (0,-1)
6.
c) y > 2x - 4
y <  2 
7.
b)
8.
c)

(2, -5)

9.
d)

(1, 1)

10.
a) No solution
11.
c)

y = -5

12.
b) parallel lines
13.
d) (1, 3)
14.
c)

(−3,  1)\left(-3,\ \ 1\right)  

15.
d) (6, -2)
16.
c) overlap each other
17.
a)

x34x^{\frac{3}{4}}

18.
a)

x35x^{\frac{3}{5}}

19.
a)

 5x\ ^5\sqrt{x}

20.
b) y = 2(4)x
21.
a) Exponential Growth
22.
b) Decay

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FAQs

What does this worksheet cover?

This Grade 9 worksheet uses 22 multiple-choice questions to practise interpreting and solving systems of linear equations and inequalities. Students match equations to graphs, determine whether ordered pairs satisfy a system, identify solution regions and points, classify systems with no solution, and solve linear systems using methods such as elimination.

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

Introduce the worksheet by reviewing how solid or dashed boundaries, shading, and inequality symbols work together in a graph. Have students explain why a test point lies inside or outside the solution region before completing the ordered-pair questions, then use the elimination and solution-count items to connect graphical reasoning with algebraic methods.

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

Watch for students choosing the wrong inequality direction when reading a shaded graph, confusing a boundary line's slope or intercept, or accepting a point that satisfies only one inequality in a system. Students may also confuse a system's intersection or solution region with an individual line and may identify parallel lines incorrectly when deciding whether a system has no solution.

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. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital quiz supports online completion and grading.

How can I differentiate this worksheet for my students?

For the 22 multiple-choice items involving graphs, equations, and ordered pairs, adjust font spacing or choose a larger font size to make the answer choices and mathematical notation easier to read. In the worksheet's Advanced Settings, you can also enable a dyslexia-friendly font or translate the worksheet into another language.

Where can I find more worksheets like this on Wayground?

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

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