Wayground
Solving Systems by Substitution - Printable Mathematics Worksheets - Wayground

Solving Systems by Substitution

10 questions

8th - 8th Grade

Mathematics

Solving Systems by Substitution is a Grade 8 mathematics worksheet that helps students find ordered-pair solutions to systems of linear equations. Across 10 items, students answer multiple-choice questions, complete a drag-and-drop vocabulary item, and enter a solution in ordered-pair form. The questions ask students to identify what a system’s solution represents, recognize when substitution is an efficient method, and solve systems such as equations written in terms of y. The worksheet also connects algebraic procedures to representations and applications. Students select systems that model word problems involving number relationships and gym pricing plans, reinforcing how two equations can describe the same situation. Use this free printable worksheet for guided practice, independent work, or a quick check of Grade 8 understanding. An answer key is included to support efficient review and feedback.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Solving Systems by Substitution

Total questions: 10

Name
Class
Date
1.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(0, 1)
2.

An ordered pair that satisfies both equations in a system of linear equations is called a ​ (a)   to the system of equations.

Choose from the below words
solution
coordinate
inconsistent
input
3.

Solve for x and y using substitution

y = 2x + 1

y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

4.
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)
5.

Solve by substitution:

y + 14 = 3x

y = -4x

Type your answer as (x, y)

(a)  

6.

Which problem would be easier to solve by substitution?

a)

y + x = 3

2y + x = 6

b)

3y - x = 7

2y = x + 6

c)

5x - 2y = 6

x + y = 2

d)

y = 2x + 2

x + y = 7

7.

Solve the following system:

2x+y=22x+y=2  


y=x−1y=x-1  

a)

(1, 0)\left(1,\ 0\right)  

b)

(4, 5)\left(4,\ 5\right)  

c)

(5, 3)\left(5,\ 3\right)  

d)

(3, 4)\left(3,\ 4\right)  

8.

Solve the following system:

y=−2y=-2  

4x−3y=184x-3y=18  

a)

(3, −2)\left(3,\ -2\right)  

b)

(3, 2)\left(3,\ 2\right)  

c)

(−2,3)\left(-2,3\right)  

d)

(2, 3)\left(2,\ 3\right)  

9.

Choose the system of linear equations that matches the word problem:

The sum of two numbers is 50. The bigger number is 5 times the smaller number. What are the two numbers?

a)

x + y = 50x\ +\ y\ =\ 50

y = x + 5y\ =\ x\ +\ 5

b)

x − y = 50x\ -\ y\ =\ 50

y = 5xy\ =\ 5x

c)

x + y = 50x\ +\ y\ =\ 50

y = 5xy\ =\ 5x

d)

x − y = 50x\ -\ y\ =\ 50

x = y + 5x\ =\ y\ +\ 5

10.

Choose the system of linear equations that matches the word problem:

Excelerated Gym offers two plans. The first plan charges members a one time fee of $25 and a $10 per class fee. The second plan charges members $20 per class. Write a system to represent the two plans?

a)

x + 25 = yx\ +\ 25\ =\ y

10y = x + 2510y\ =\ x\ +\ 25

b)

10x +25 = y10x\ +25\ =\ y

y =20xy\ =20x

c)

x + y = 20x\ +\ y\ =\ 20

y + 10= 25xy\ +\ 10=\ 25x

d)

10x − 25 = y10x\ -\ 25\ =\ y

x = 20yx\ =\ 20y

Answer Key

Solving Systems by Substitution

Total questions: 10

1.
a) (1, -1)
2.
solution
3.
a)

(1,3)

4.
b) the intersection of the two equations on a graph
5.
(2, -8), 2, -8
6.
d)

y = 2x + 2

x + y = 7

7.
a)

(1, 0)\left(1,\ 0\right)  

8.
a)

(3, −2)\left(3,\ -2\right)  

9.
c)

x + y = 50x\ +\ y\ =\ 50

y = 5xy\ =\ 5x

10.
b)

10x +25 = y10x\ +25\ =\ y

y =20xy\ =20x

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Solving Systems by Substitution worksheet cover?

This Grade 8 worksheet develops the skill of solving systems of linear equations by substitution and reporting the solution as an ordered pair. Its 10 items combine multiple-choice questions with a drag-and-drop definition and a fill-in response, asking students to identify the intersection that represents a solution, choose a system suited to substitution, solve equations, and match word problems with systems.

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

First model how to substitute an expression for one variable into the other equation, then solve and write the result as an ordered pair. Use the worksheet’s questions about equations already written in terms of y to discuss why those systems are efficient for substitution, and have students check whether their ordered pair satisfies both equations. Finish with the number and gym-plan word problems so students connect the procedure to writing systems from real situations.

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

Watch for students confusing a coordinate or input with a solution, or identifying a y-intercept or slope instead of the intersection of the two equations. In the substitution items, students may substitute without preserving the equation’s sign, solve for only one variable, or reverse the coordinates when entering an answer as (x, y). For the word-problem items, check that students translate both relationships into equations before selecting a system.

How do I assign and grade this worksheet?

The Solving Systems by Substitution worksheet is available as a printable PDF and as a digital quiz on Wayground. It includes a complete answer key for the multiple-choice, drag-and-drop, and fill-in items, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support classrooms that are reducing screen time.

How can I differentiate this systems-by-substitution worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the equations, ordered-pair choices, and word-problem text are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options support access to the substitution tasks.

Where can I find more free 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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion