Wayground
System of Two Equations - Printable Mathematics Worksheets - Wayground

System of Two Equations

15 questions

8th Grade

Mathematics

This Grade 8 mathematics worksheet gives students 15 multiple-choice questions on systems of two linear equations. Students determine solutions algebraically, identify ordered pairs that satisfy a system, interpret graphs and estimated intersection points, classify graphs as parallel or coinciding, recognize equivalent equation systems, and connect a real-world materials-purchase situation to its equations and solution. The worksheet also reviews graphing methods, including two points, x- and y-intercepts, and slope with y-intercept. Its varied questions help students connect equations, ordered pairs, lines, slopes, intercepts, and intersections rather than relying on a single solving procedure. Use this free printable worksheet for Grade 8 mathematics practice, independent work, review, or a formative check, and use the included answer key to evaluate student understanding.

Worksheet settings

Font size

S
M
L
XL
Worksheets

System of Two Equations

Total questions: 15

Name
Class
Date
1.

What is the solution to this system of linear equations?y - 3x = 0 and y = 3x

a)

The only solution is (0, 3).

b)

There is no solution.

c)

The only solution is (0, 0).

d)

There are infinitely many solutions.

2.

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

3.

Which system of linear equations is shown on the graph?

a)

y= 4x-2 and y=1/4x-2

b)

y=-1/4x-2 and y=-4x-2

c)

y=1/4x-2 and y=-4x-2

d)

y=-1/4x-2 and y=4x-2

4.

The graphs of two linear equations are shown. What is the best estimate of the solution to the system of equations?

a)

(0, 2)

b)

(2, 0)

c)

(2, -2)

d)

(-2, -2)

e)

(-2, 2)

5.

The graphs of two linear equations are shown. What is the best estimate of the solution to the system of linear equations?

a)

(2, -5)

b)

(5, -2)

c)

(-5, -2)

d)

(-2, 5)

e)

(-2, -5)

6.

The graphs of two linear equations are shown. What is the best estimate of the solution to the system of linear equations?

a)

(0, 3)

b)

(3, 0)

c)

(0, -3)

d)

(-3, 3)

e)

(-3, 0)

7.

Which of the following ordered pairs is the solution of the system:

a)

(3, 2)

b)

(4, 1)

c)

(5, 0)

d)

(6, -1)

8.

Eulah wants to buy materials for her Math project. If she buys an illustration board and a marker, she needs to pay P 22.00. But if she buys 2 illustration boards and a marker she will pay P 37.00. What is the system of the linear equations in the problem?

a)

a.

b)

b.

c)

c.

d)

d.

9.

How do you describe the graphs of the system?

a)

coinciding lines

b)

intersecting lines

c)

parallel lines

d)

skew lines

10.

Which of the following illustrates a system of linear equations in two variables?

a)

2x−y>12x-y>1   y=2x2−1y=2x^2-1  

b)

x+y=0x+y=0   8y>x−648y>x-64  

c)

x−7<2yx-7<2y   y=5x−1y=5x-1  

d)

x−y=4x-y=4   y=x+2y=x+2  

11.

Eulah wants to buy materials for her Math project. If she buys an illustration board and a marker, she needs to pay P 22.00. But if she buys 2 illustration boards and a marker she will pay P 37.00. What ordered pair will make the equations true?

a)

(5, 17)

b)

(10, 12)

c)

(15, 7)

d)

(20, 2)

12.

Which of the following methods can be used in graphing system of linear equations in two variables?

a)

two points

b)

x and y – intercepts

c)

slope and y- intercept

d)

all of the above

13.

Which of the following is correct when the system is graphed using a slope and y-intercept method?

a)

Equation1:m=2,b=−2Equation1:m=2,b=-2   Equation2:m=2,b=−1Equation2:m=2,b=-1  

b)

Equation1:m=−2,b=2Equation1:m=-2,b=2   Equation2:m=−2,b=1Equation2:m=-2,b=1  

c)

Equation1:m=12,b=−1Equation1:m=\frac{1}{2},b=-1   Equation1:m=12,b=−2Equation1:m=\frac{1}{2},b=-2  

d)

Equation1:m=−12,b=2Equation1:m=-\frac{1}{2},b=2   Equation1:m=−12,b=1Equation1:m=-\frac{1}{2},b=1  

14.

What is the graph of the system?

a)
b)
c)
d)
15.

Which of the following is true about the graph of the system?

a)

The slopes are the same.

b)

The slopes are different.

c)

The y-intercepts are the same.

d)

There is a point of intersection.

Answer Key

System of Two Equations

Total questions: 15

1.
d)

There are infinitely many solutions.

2.
c)

y = -5

3.
c)

y=1/4x-2 and y=-4x-2

4.
e)

(-2, 2)

5.
b)

(5, -2)

6.
b)

(3, 0)

7.
a)

(3, 2)

8.
a)

a.

9.
c)

parallel lines

10.
d)

x−y=4x-y=4   y=x+2y=x+2  

11.
c)

(15, 7)

12.
d)

all of the above

13.
d)

Equation1:m=−12,b=2Equation1:m=-\frac{1}{2},b=2   Equation1:m=−12,b=1Equation1:m=-\frac{1}{2},b=1  

14.
d)
15.
a)

The slopes are the same.

Browse by subjects

Browse by grades

Browse by format

FAQs

What does this systems of two equations worksheet cover?

This Grade 8 worksheet uses 15 multiple-choice questions to practice solving and interpreting systems of two linear equations. Students identify solutions and ordered pairs, read intersection points from graphs, distinguish parallel and coinciding lines, select equations from graphs, and model a materials-purchase situation with a system and its solution.

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

Use the questions to move from representation to interpretation: review how two equations form two lines, then have students connect slopes and y-intercepts to the graphs before selecting a solution or estimated intersection. Discuss why identical lines have infinitely many solutions and why parallel lines have none, then use the materials-purchase items to show how a situation becomes a system and how an ordered pair can be checked in both equations.

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

Watch for students reversing the coordinates of an ordered pair when reading an intersection, choosing a nearby graph point instead of the actual or best-estimated intersection, or confusing parallel lines with coinciding lines. Students may also mistake equal slopes for a single intersection, select an equation with the wrong sign or intercept, or choose a materials-price pair without checking that it satisfies both equations.

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

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the 15 multiple-choice questions in the format that suits your lesson. 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 worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the multiple-choice options and graph-based prompts easier to read. You can also select a dyslexia-friendly font or translate the worksheet into another language while keeping the systems-of-equations practice intact.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive 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.

© 2026 Wayground Inc.

Accessibility and Inclusion