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Algebra 1 Test -- System of Equations Part 1 - Printable Mathematics Worksheets - Wayground

Algebra 1 Test -- System of Equations Part 1

25 questions

8th - 10th Grade

Mathematics

Algebra 1 Test -- System of Equations Part 1 is a free printable mathematics worksheet for students in Grades 8–10. It contains 25 multiple-choice questions that assess solving systems of linear equations, identifying ordered-pair solutions, and distinguishing one solution, no solution, and infinitely many solutions from the relationships between two lines. Students also practice rewriting an equation in slope-intercept form and recalling the steps for graphing a line, including plotting the y-intercept and using the slope to locate another point. Questions use equations, graph-based representations, and conceptual statements, giving teachers a focused check of both procedural understanding and interpretation of line intersections. A complete answer key is included for efficient review, grading, or reteaching.

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Worksheets

Algebra 1 Test -- System of Equations Part 1

Total questions: 25

Name
Class
Date
1.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
2.

What is the solution?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

3.

A system of equations with no solution will have lines that...

a)

are the same

b)

cross in one place

c)

are parallel and never touch

4.

A system of equations with infinitely many solutions will have lines that...

a)

are the same

b)

cross in one place

c)

are parallel and never touch

5.
What is the solution to this system?
x - y = 6
y= 2x - 5
a)
(1,3)
b)
(-1,3)
c)
(-1,-7)
d)
(1,-7)
6.
Solve:
y = 7x + 9
2y + 2x = -18
a)
(5, 0)
b)
(9, 18)
c)
(-2, -5)
d)
(1, 16)
7.
Solve for x and y
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
8.
What is the first step in solving a system by graphing?
a)
Write both linear equations in slope-intercept form
b)
Get x by itself
c)
Compare the slopes of both equations
d)
Write both equations in standard form
9.
The solution to a system of equations is any ordered pair that makes both equations true. 
a)
TRUE
b)
FALSE
10.
What is the solution? 
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
11.
What is the
slope-intercept form
of the equation
-8x+2y=4
a)
none
b)
y=2-4x
c)
y=4x+2
d)
y=4x-8y
12.
What are the steps for graphing a line?
a)
1. Plot y-intercept
2. count slope ratio plot second point
3. Draw the line.
b)
1. Make a table
2. Plot slope
3. Draw line
c)
1. Plot two points
2. Check slope
3. Draw line
d)
1. Draw line
2. Hope it is right
13.

What is the solution to the graph shown?

a)

no solution

b)

infinitely many solutions

c)

2/3

d)

(0,-3)

14.
If a system of linear equations has one solution, what does this mean about the two lines? 
a)
Parallel lines
b)
the same line 
c)
Intersecting lines
15.
What is the solution to this equation?
a)
one solution
b)
no solution
c)
infinite solutions
d)
none of these
16.
How can you tell if a point is a solution to a system?
a)
It makes the first equation true.
b)
The (x,y) coordinates satisfy both equations
c)
It makes logical sense
d)
It makes neither equation negative
17.
x = x
a)
No Solution
b)
One Solution
c)
Infinite Solutions
d)
Beyond Solutions
18.
What is the solution to this system of equations?
a)
(4, -1)
b)
(-1, 4)
c)
(-4, 1)
d)
(-4, -1)
19.
If you were to plot the point (4, -12) what would be the correct method?
a)
Up 4, left 12
b)
Right 4, up 12
c)
Down 4, left 12
d)
Right 4, down 12
20.
Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4
a)
YES
b)
NO
21.

What letter is at (-3,7)

a)

There is no letter at those coordinates.

b)

T

c)

E

d)

H

22.
Find the slope
a)
4/5
b)
5/4
c)
-5/4
d)
-4/5
23.

What letter is at (-2,6)?

a)

There is no letter at those coordinates.

b)

T

c)

E

d)

H

24.

What letter is at (3,3)?

a)

There is no letter at those coordinates.

b)

V

c)

O

d)

H

25.
What is the solution to the system?
a)
(6, 8)
b)
(8, 6)
c)
(-6, 8)
d)
No solution
Answer Key

Algebra 1 Test -- System of Equations Part 1

Total questions: 25

1.
a) (6, 3)
2.
b)

No solution

3.
c)

are parallel and never touch

4.
a)

are the same

5.
c) (-1,-7)
6.
c) (-2, -5)
7.
a) (1,3)
8.
a) Write both linear equations in slope-intercept form
9.
a) TRUE
10.
d) (1, -1)
11.
c) y=4x+2
12.
a) 1. Plot y-intercept
2. count slope ratio plot second point
3. Draw the line.
13.
b)

infinitely many solutions

14.
c) Intersecting lines
15.
b) no solution
16.
b) The (x,y) coordinates satisfy both equations
17.
c) Infinite Solutions
18.
a) (4, -1)
19.
d) Right 4, down 12
20.
a) YES
21.
c)

E

22.
a) 4/5
23.
b)

T

24.
a)

There is no letter at those coordinates.

25.
a) (6, 8)

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FAQs

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

This 25-question multiple-choice worksheet focuses on solving systems of linear equations and interpreting their graphs. Students identify ordered-pair solutions, classify systems as having one, no, or infinitely many solutions, rewrite equations in slope-intercept form, and apply the basic steps for graphing lines. Together, these items connect algebraic solutions with intersecting, parallel, or identical lines.

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

Use the graphing-focused questions to establish the sequence: rewrite each equation in slope-intercept form, plot the y-intercept, use the slope to plot another point, and draw each line. Then have students explain how the graph reveals the system’s solution: an intersection gives one solution, parallel lines give no solution, and the same line gives infinitely many solutions. Pause before assigning the full set to ask students why an ordered pair must make both equations true.

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

Watch for students selecting a single x- or y-value instead of an ordered pair, or accepting a pair without checking it in both equations. Students may also confuse parallel lines with identical lines, leading them to switch no solution and infinitely many solutions. When rewriting equations such as -8x + 2y = 4, check that students isolate y and preserve the correct signs before graphing.

How do I assign and grade this worksheet?

This systems of equations worksheet is available as a printable PDF and 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. The printable format can also support schools that are reducing screen time.

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

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the multiple-choice equations, ordered-pair options, and graphing prompts are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate. These changes create an alternate version of the same systems-of-equations practice.

Where can I find more 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.

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