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Solving Systems of Equations - Algebra 1 - Printable Mathematics Worksheets - Wayground

Solving Systems of Equations - Algebra 1

15 questions

8th - 8th Grade

Mathematics

Solving Systems of Equations - Algebra 1 is a Grade 8 mathematics worksheet with 15 multiple-choice questions focused on solving and interpreting linear equations and systems. Students use substitution, elimination, and graphing to find ordered-pair solutions, identify the intersection of two lines, determine whether a system has one, no, or infinitely many solutions, and find a requested coordinate value. The worksheet also checks related skills, including identifying input and output variables, testing points in an inequality or system of inequalities, and recognizing whether a point is or is not a solution. These varied questions help teachers assess both procedural fluency and foundational understanding of linear relationships. This free printable worksheet includes a complete answer key for efficient review, independent practice, or classroom assessment.

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Worksheets

Solving Systems of Equations - Algebra 1

Total questions: 15

Name
Class
Date
1.

Solve the system of equations with substitution 6x+2y=0, y=2x−56x+2y=0,\ y=2x-5  

a)

(-2,-9)

b)

(1,-3)

c)

(2,3)

d)

(-1,-7)

2.

Solve the system of equations with elimination y=2x+6, 2y=2x+4y=2x+6,\ 2y=2x+4  

a)

(3,12)

b)

(6,6)

c)

(6,18)

d)

(-6,-6)

3.

What is the answer to a system of equations?

a)

The slope of both lines

b)

The point where the line crosses the y-axis

c)

The point where the two lines intersect

d)

The points where the lines intersect the x-axis

4.

Solve the system of equations by graphing.
 y=−4x+5, y=3x−16y=-4x+5,\ y=3x-16  

a)

(-3, -25)

b)

(3,-7)

c)

(11, 17)

d)

(21, 47)

5.

What is the solution to this equation?

a)

(1, -1)

b)

(2, 0)

c)

(0, -2)

d)

(0, 1)

6.

How many solutions does a system with two parallel lines have?

a)

0

b)

1

c)

2

d)

Infinitely many

7.

How many solutions does this system have? y=2x+6, 2y=4x+12y=2x+6,\ 2y=4x+12  

a)

1 solution

b)

infinite solutions

c)

no real solutions

8.

Solve the system of equations by substitution. y=4x, 6x−4y=−10y=4x,\ 6x-4y=-10  

a)

(1, -4)

b)

(1, 4)

c)

(-4, -7)

d)

(-7, -4)

9.

Solve the system of equations.

5x + 3y = 7, y = 4

a)

(4,1)

b)

(4,-1)

c)

(1,4)

d)

(-1,4)

10.
Which point is a solution to the inequality? 
4x - 3y ≥ 18 
a)
(0, -6) 
b)
(0, 0) 
c)
(2, 2) 
d)
(-4, 6) 
11.

What is the input in this equation?

y = 4x + 16

a)

4

b)

y

c)

16

d)

x

12.

What is the output in this equation?

7y + 4x = 10

a)

y

b)

7

c)

x

d)

10

13.

Which is not a solution to this system of inequalities?

a)

(0,-1)

b)

(0,3)

c)

(4,0)

d)

(6,-2)

14.

What is the y value in the solution to this system of equations?

x - 2y = 1, x + 4y = 7

a)

1

b)

-1

c)

3

d)

4

15.

How many solutions does a system of equations where the lines are on top of each have?

a)

two solutions

b)

one solution

c)

infinite solutions

d)

no solutions

Answer Key

Solving Systems of Equations - Algebra 1

Total questions: 15

1.
b)

(1,-3)

2.
d)

(-6,-6)

3.
c)

The point where the two lines intersect

4.
b)

(3,-7)

5.
a)

(1, -1)

6.
a)

0

7.
b)

infinite solutions

8.
b)

(1, 4)

9.
d)

(-1,4)

10.
a) (0, -6) 
11.
d)

x

12.
a)

y

13.
a)

(0,-1)

14.
a)

1

15.
c)

infinite solutions

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FAQs

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

This 15-question multiple-choice worksheet practices solving systems by substitution, elimination, and graphing, then interpreting solutions as ordered pairs where lines intersect. It also asks students to identify systems with one, no, or infinitely many solutions and to find specific coordinate values, building both method fluency and conceptual understanding.

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

Introduce the meaning of a system’s solution as the point that satisfies both equations, then model one item with substitution, one with elimination, and one by graphing. As students work through the multiple-choice questions, ask them to explain why a selected ordered pair works in both equations and how parallel or coincident lines change the number of solutions.

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

Watch for sign errors when students substitute expressions or eliminate a variable, and for selecting an x- or y-value without finding the requested ordered pair or coordinate. Students may also confuse parallel lines, which have no solution, with coincident lines, which have infinitely many solutions, or fail to test both inequalities when deciding whether a point is a solution.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for checking all 15 multiple-choice items. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation choices and ordered pairs are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while preserving its multiple-choice format.

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, including 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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