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Solve the System of Equations by Substitution or Elimination - Printable Mathematics Worksheets - Wayground

Solve the System of Equations by Substitution or Elimination

15 questions

8th - 8th Grade

Mathematics

This Grade 8 mathematics worksheet gives students focused practice solving systems of two linear equations using substitution and elimination. Across 15 multiple-choice questions, students solve for ordered pairs, identify what it means to substitute or eliminate, and determine whether a system has one solution, no solution, or infinitely many solutions. The worksheet is useful for guided practice, independent review, or a quick check of understanding after instruction on systems of equations. Students must select the correct solution from plausible options, helping teachers identify errors such as choosing the wrong ordered pair or misapplying a method. It is a free printable worksheet with a complete answer key for efficient checking.

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Solve the System of Equations by Substitution or Elimination

Total questions: 15

Name
Class
Date
1.

Solve the solution by substitution:

x = 7 - 2y

2x + y = 5

a)

(-1,4)

b)

(4,-1)

c)

(1,3)

d)

(3,1)

2.

Solve the system by substitution:

x - y = 6

y - 2x = - 5

a)

(1,3)

b)

(-1,3)

c)

(-1,-7)

d)

(1,-7)

3.
Solve by elimination:
7x+y=-9

-3x-y=5
a)
No solution
b)
(1,8)
c)
(-2,-3)
d)
(-1,-2)
4.
Solve by elimination:
-x+2y=17

2x+2y=-10
a)
ARN
b)
(-9,4)
c)
(-9,-4)
d)
(9,-4)
5.
What is the solution to this system? Solve by substitution.
y= 4x + 3
2x - 3y = 21
a)
(3,-9)
b)
(-3,-9)
c)
(-3,9)
d)
(0,1)
6.

Solve the system by elimination.


7x - y = -10

-7x + 5y = -6

a)

(-2, -4)

b)

(-2, -1)

c)

(-4, -1)

d)

(6, -8)

7.
What does it mean to substitute?
a)
to remember
b)
to replace or to plug in
c)
to get rid of or to take away
d)
to connect the dots
8.
Solve by using substitution method.
a)
(2, 7)
b)
(0, 1)
c)
(2/5, 9/5)
d)
(2, 5)
9.
What does it mean to eliminate?
a)
to remember
b)
to replace or to plug in
c)
to get rid of or to take away
d)
to connect the dots
10.
Solve by using elimination method.
a)
(3, 1)
b)
( 5, -5)
c)
(2, 5)
d)
(15, 1)
11.
Solve the system of Equation (x,y)
x + 3y = 18
 –x –4y = –25 
a)
(3,7)
b)
(-3,7)
c)
(7,-3)
d)
(-3,-7)
12.

Solve the system of equations.

a)

(11, 21)

b)

(3, 11)

c)

(11, -67)

d)

No solution

e)

Infinite solutions

13.

Solve the system of equations.

a)

(10, 3)

b)

(6, 3)

c)

(15, 3)

d)

No solution

e)

Infinite Solution

14.

How many solutions will this system have?

a)

one solution

b)

no solution

c)

infinitely many solutions

15.

How many solutions will this system have?

a)

one solution

b)

no solution

c)

infinitely many solutions

Answer Key

Solve the System of Equations by Substitution or Elimination

Total questions: 15

1.
c)

(1,3)

2.
c)

(-1,-7)

3.
d) (-1,-2)
4.
b) (-9,4)
5.
b) (-3,-9)
6.
a)

(-2, -4)

7.
b) to replace or to plug in
8.
d) (2, 5)
9.
c) to get rid of or to take away
10.
a) (3, 1)
11.
b) (-3,7)
12.
a)

(11, 21)

13.
b)

(6, 3)

14.
b)

no solution

15.
a)

one solution

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FAQs

What does this worksheet cover, and how does it help students solve systems of equations?

This Grade 8 worksheet contains 15 multiple-choice questions on solving systems of two linear equations by substitution and elimination. Students select ordered-pair solutions, distinguish the meanings of “substitute” and “eliminate,” and classify systems as having one solution, no solution, or infinitely many solutions.

How can I use this worksheet to teach solving systems by substitution and elimination?

Introduce the two methods with one worked system, modeling how to replace a variable through substitution and how to cancel a variable through elimination. Then have students explain which method each problem uses and justify the ordered pair they select; use the vocabulary items and solution-count questions to reinforce the meaning of each method before independent completion.

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

Watch for students reversing the coordinates in an ordered pair, making a sign error when substituting a negative expression, or combining equations incorrectly during elimination. Students may also confuse “no solution” with “infinitely many solutions,” so ask them to check whether the equations intersect once, never intersect, or represent the same line.

How do I assign and grade this worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this systems of equations worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the 15 multiple-choice systems and answer choices easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those file-level options support access to the substitution, elimination, and solution-count questions.

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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