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Systems of Linear Equations (Substitution) - Printable Mathematics Worksheets - Wayground

Systems of Linear Equations (Substitution)

9 questions

8th - 8th Grade

Mathematics

Systems of Linear Equations (Substitution) is a Grade 8 mathematics worksheet that helps students solve systems by replacing one variable expression with its equivalent from the other equation. The nine multiple-choice questions begin by identifying a system’s solution as the intersection of two equations and then require students to determine ordered-pair solutions, including a system with no solution. Students practice substituting expressions for x or y, simplifying the resulting one-variable equation, and checking both original equations before selecting an answer. The varied equation forms and ordered-pair choices help reinforce accuracy with signs, coordinate order, and algebraic operations. This free printable worksheet includes a complete answer key and is suitable for guided practice, independent work, review, or a quick assessment after instruction on substitution.

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Worksheets

Systems of Linear Equations (Substitution)

Total questions: 9

Name
Class
Date
1.

The solution of a system of linear equations is...

a)

the y-intercept (b)

b)

the intersection of the two equations on a graph

c)

the second equations' answers

d)

the slope (m)

2.
Solve the system of equations using substitution:
4x - 2y = 6
y = 3x - 3
a)
(3, 6)
b)
(-7, 1)
c)
(0, -3)
d)
(2, 3)
3.

Solve the system of equations.

y = 4x + 1

3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

4.

Solve using substitution

2x + y = 9

y = 5x + 2

a)

(1,7)

b)

(2,5)

c)

(-1,-3)

d)

(5,-1)

5.

Solve using substitution

y = 4x + 3

2x - 3y = 21

a)

(3,-9)

b)

(-3,-9)

c)

(-3,9)

d)

(0,1)

6.

Solve using substitution

x = 7 - 2y

2x + y = 5

a)

(-1,4)

b)

(4,-1)

c)

(1,3)

d)

(3,1)

7.

Solve using substitution

3x + 5y = 10

x = y + 6

a)

(4, 1)

b)

(5, -1)

c)

(4, -1)

d)

(5, 1)

8.

Solve using substitution

x + 7y = 6

-2x + 2y = 4

a)

(-1,1)

b)

(-6,-1)

c)

(-1,-6)

d)

(-1,6)

9.

Solve using substitution

4x + y = 6

8x + 2y = -8

a)

(-8,-1)

b)

(-1,-8)

c)

(1,-8)

d)

No Solution

Answer Key

Systems of Linear Equations (Substitution)

Total questions: 9

1.
b)

the intersection of the two equations on a graph

2.
c) (0, -3)
3.
a)

(1, 5)

4.
a)

(1,7)

5.
b)

(-3,-9)

6.
c)

(1,3)

7.
b)

(5, -1)

8.
a)

(-1,1)

9.
d)

No Solution

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FAQs

What does this systems of linear equations worksheet cover?

This Grade 8 worksheet covers solving systems of linear equations by substitution through nine multiple-choice questions. Students identify a system’s solution as the graph intersection, substitute expressions for x or y, solve for the remaining variable, and select the correct ordered pair or recognize when a system has no solution.

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

Model one item by replacing the given expression for y or x in the second equation, solving the resulting one-variable equation, and substituting back to find the ordered pair. Then have students explain which equation they substituted into and verify their selected pair in both equations, using the final item to discuss why equivalent equations can produce no solution.

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

Watch for students reversing the ordered pair, dropping a negative sign during substitution, or stopping after finding only one variable. Students may also select a pair that satisfies one equation but not both, or overlook that the final system has no solution; checking each candidate in both original equations helps reveal these errors.

How do I assign and grade this systems of equations worksheet?

On Wayground, assign Systems of Linear Equations (Substitution) as a printable PDF or as a digital quiz, and use its complete answer key to grade the nine multiple-choice items. Printable submissions can also be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this substitution worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the equation pairs and ordered-pair choices are easier to read. You can also apply a dyslexia-friendly font or translate the substitution questions into another language when that better supports access to the algebra practice.

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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