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Elimination System of Equations - Printable Mathematics Worksheets - Wayground

Elimination System of Equations

15 questions

8th - 8th Grade

Mathematics

Elimination System of Equations is a Grade 8 mathematics worksheet with 15 multiple-choice questions focused on solving systems of linear equations. Students determine ordered-pair solutions, identify where two lines intersect, and work with equations written in standard, slope-intercept, or mixed forms. Several items also ask students to translate real-world situations—such as rental costs, sports statistics, and changing bank balances—into systems and select the solution that fits the context. This free printable worksheet helps students build accuracy with elimination-based reasoning while checking whether a solution satisfies both equations. It is useful for guided practice, independent review, or a formative assessment after introducing systems of equations. The worksheet includes a complete answer key so teachers can review computation, equation modeling, and interpretation of solutions efficiently.

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Worksheets

Elimination System of Equations

Total questions: 15

Name
Class
Date
1.
-8x - 7y = 10
-8x + 5y = 34
answers in (x,y)
a)
No Solution
b)
(-3, -10)
c)
(3, 2)
d)
(-3, 2)
2.
-2x + y = 1
-4x + y =- 1
answers in (x,y)
a)
(1,3)
b)
no solution
c)
(-1,3)
d)
(3,1)
3.
-3x+3y = 18
5x-3y = -26
answers in (x,y)
a)
(4,2)
b)
(-4,-2)
c)
(-4,2)
d)
(4,-2)
4.

Solve the system of equations:

y=2x

x + y = 9

a)

(6, 3)

b)

(3, 6)

c)

(-3, -6)

d)

no solution

5.

Solve the system of equations:

7x+2y=24

8x+2y=30

a)

(6,-9)

b)

(-9,6)

c)

(-6,9)

d)

(0,0)

6.

Solve the system of equations:

y = -2x + 18

y = 8

a)

(5, 8)

b)

(-5, 8)

c)

(2, 8)

d)

(-2, 8)

7.

Your friend rents 10 chairs and 2 tables for $300. Another friend rents 8 chairs and 4 tables for $360. How much does a chair and a table cost? Write a system of equations to solve.

a)

Chairs $2 Tables $5

b)

Chairs $50 Tables $20

c)

Chairs $10 Tables $15

d)

Chairs $20 Tables $50

8.

Solve the system of equations:

3x + y = –21

x + y = –5

a)

(-3,8)

b)

(8,-3)

c)

(3,-8)

d)

(-8,3)

9.
Where do these lines intersect?
x-y=11
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(3,-4)
d)
(6,7)
10.

Solve the system of equations below:

2x+3y=42x+3y=4  

3x−2y=193x-2y=19  

a)

(5,−2)\left(5,-2\right)  

b)

(−5,−2)\left(-5,-2\right)  

c)

(−5,2)\left(-5,2\right)  

d)

(5,2)\left(5,2\right)  

11.

Solve the system of equations below:

7x+5y=−177x+5y=-17  

2x+2y=−62x+2y=-6  

a)

(−1,−2)\left(-1,-2\right)  

b)

(−1,2)\left(-1,2\right)  

c)

(1,−2)\left(1,-2\right)  

d)

(1,2)\left(1,2\right)  

12.
Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 
a)
x + y = 1550
y  = 4x
b)
x + y = 1550
y = x + 4
c)
y - x = 1550
y = 4x
d)
y = 1550 + x
y = x + 4
13.
Solve the system:
x + 6y = 17
x - 3y = 8
a)
(5, 2)
b)
(11, 1)
c)
(1, 11)
d)
no solution
14.

8x + 14y = 4

-6x - 7y = -10

a)

(4, -2)

b)

(-2, 4)

c)

(0, 3)

d)

(-4, -2)

15.

Macy starts with $20 in her bank account and she saves $5 each week. Robby has $100 in his bank account, and he saves $2.50 each week. After how many weeks will Macy and Robby have the same amount in their accounts and how much money will that be? Write a system of equations to solve.

a)

25 weeks; $160

b)

32 weeks; $180

c)

20 weeks; $120

d)

22 weeks; $135

Answer Key

Elimination System of Equations

Total questions: 15

1.
d) (-3, 2)
2.
a) (1,3)
3.
c) (-4,2)
4.
b)

(3, 6)

5.
a)

(6,-9)

6.
a)

(5, 8)

7.
d)

Chairs $20 Tables $50

8.
d)

(-8,3)

9.
a) (10,-1)
10.
a)

(5,−2)\left(5,-2\right)  

11.
a)

(−1,−2)\left(-1,-2\right)  

12.
a) x + y = 1550
y  = 4x
13.
b) (11, 1)
14.
a)

(4, -2)

15.
b)

32 weeks; $180

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FAQs

What does the Elimination System of Equations worksheet cover?

This Grade 8 worksheet provides 15 multiple-choice problems on solving systems of linear equations, primarily by eliminating a variable and identifying the resulting ordered pair. Students also interpret solutions as line intersections and select systems that model situations involving prices, running yards, and savings accounts. Completing these items reinforces accurate elimination, substitution when equations are already simplified, and checking that a pair satisfies both equations.

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

Introduce the worksheet by modeling how adding or subtracting the two equations can remove one variable, then solve for the remaining variable and substitute back. Use the items with equations such as 7x + 2y = 24 and 8x + 2y = 30 to discuss aligning like terms and tracking signs. After students solve a few symbolic systems, have them explain how the ordered pair represents the intersection of the two lines and apply the same process to the word problems.

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

Watch for sign and subtraction errors when students eliminate a variable, especially with negative coefficients, and for stopping after finding only one variable. Students may also reverse the ordered pair, confuse a solution with a no-solution choice, or choose an answer that satisfies only one equation. In the chair-and-table, football-yardage, and bank-account problems, check that students translate the relationships correctly before solving.

How do I assign and grade this worksheet?

The Elimination System of Equations worksheet is available as a printable PDF and as a digital quiz on Wayground. It includes a complete answer key for checking the 15 multiple-choice responses, 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 does this worksheet help students model real-world systems of equations?

Three multiple-choice items ask students to connect systems of equations to real situations: the costs of chairs and tables, two football players’ combined rushing yards, and two savings plans reaching the same balance. Students must identify variables, represent totals or relationships with equations, and interpret the resulting solution in units such as dollars, yards, or weeks. These items extend elimination practice beyond isolated equations and reveal whether students understand what each variable represents.

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 support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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