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System of Equation Elimination - Printable Mathematics Worksheets - Wayground

System of Equation Elimination

10 questions

8th Grade

Mathematics

System of Equation Elimination is a Grade 8 mathematics worksheet with 10 multiple-choice questions focused on solving pairs of linear equations by elimination. Students determine ordered-pair solutions by combining or subtracting equations, including systems with coefficients that cancel directly and systems requiring elimination of one variable. The questions also ask students to recognize when a system has infinitely many solutions or no solution, rather than selecting an ordered pair. This free printable worksheet supports independent practice, review, or a quick assessment of students’ accuracy with elimination, sign management, and interpreting solution types. It includes a complete answer key for checking student work and guiding follow-up instruction.

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System of Equation Elimination

Total questions: 10

Name
Class
Date
1.

−4x − 4y = 0
4x + 4y = 0 

a)

(−6, −4) 

b)

Infinite number of solutions  

c)

(−6, 10) 

d)

(6, 4) 

2.

Solve the system by elimination.  

−8x − 10y = 20
−8x − 6y = −4 

a)

Infinite number of solutions  

b)

(6, 5) 

c)

(−6, −5) 

d)

(5, −6) 

3.

Solve by elimination
-2x + 6y = 16
-4x - 3y = 2

a)

(2,2)

b)

(-2, -2)

c)

(-2,2)

d)

(2,1)

4.

 4x + 8y = 20
-4x + 2y = -30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

5.

Solve by elimination:
9x-4y=7

x-4y=-17

a)

(-1,5)

b)

(-7,5)

c)

(7,5)

d)

(3,5)

6.

x - y=11

2x+y=19

a)

(10,-1)

b)

(-1,10)

c)

(3,-4)

d)

(6,7)

7.

Solve the system by elimination. 
 −4x − 4y = 0
4x + 4y = 0 

a)

(−6, −4) 

b)

Infinite number of solutions  

c)

(−6, 10) 

d)

(6, 4) 

8.

3x  - 3y = 33
6x - 3y = 57

a)

(8,-3)

b)

(-3,8)

c)

(10,1)

d)

(10,-1)

9.

Solve by elimination:
7x-9y=29

7x+2y=-15

a)

(-4,-1)

b)

(-1.-4)

c)

(-1,4)

d)

(-1,6)

10.

-4x - 6y = 6
4x + 6y = -4

a)

no solution

b)

(2,0)

c)

(-4,0)

d)

(0,0)

Answer Key

System of Equation Elimination

Total questions: 10

1.
b)

Infinite number of solutions  

2.
d)

(5, −6) 

3.
c)

(-2,2)

4.
d)

(7,-1)

5.
d)

(3,5)

6.
a)

(10,-1)

7.
b)

Infinite number of solutions  

8.
a)

(8,-3)

9.
b)

(-1.-4)

10.
a)

no solution

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FAQs

What does this system of equation elimination worksheet cover?

This Grade 8 worksheet contains 10 multiple-choice problems in which students solve systems of two linear equations using elimination. It builds fluency with eliminating a variable, identifying ordered-pair solutions, and recognizing systems with infinitely many solutions or no solution, as shown in the repeated and opposing-equation cases.

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

Model one problem by adding or subtracting the equations to cancel a variable, then substitute back to verify the ordered pair. Use the worksheet’s systems with matching or opposite equations to discuss why some pairs have infinitely many solutions or no solution before students complete the remaining multiple-choice items independently.

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

Students may make sign errors when combining equations, report a value for only one variable, or choose a distractor without checking the ordered pair in both original equations. They may also treat equations that represent the same relationship as having one solution, or overlook that opposite equations can produce no solution.

How do I assign and grade this system of equation elimination worksheet?

Assign it as a printable PDF or as a digital quiz on Wayground, depending on whether students should show work on paper or respond online. The worksheet 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?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation pairs and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the elimination problems and instructions into another language when appropriate.

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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