Grade 8 Systems of Equations Quiz – Free PDF

Contents

This grade 8 systems of equations quiz asks 10 multiple-choice questions on systems of linear equations, and each answer comes with a short explanation.

Ten multiple-choice questions check your skill with systems of linear equations: reading intersections, testing ordered pairs, substitution, elimination, no-solution systems and word problems. Choose the one correct answer, then read the explanation to learn from any mistake.

Grade 8Common Core: 8.EE.C.8a · 8.EE.C.8b · 8.EE.C.8c

🎯 Systems of Linear Equations – Grade 8 math quiz

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Question 1

The graph shows the system $y=x+1$ and $y=-x+5$. What is the solution?

The lines cross at point A.

A $(3,2)$

B $(2,3)$

C $(0,1)$

D $(0,5)$

Question 2

Which ordered pair satisfies both $y=3x+1$ and $x+y=5$?

A $(1,4)$

B $(0,1)$

C $(2,3)$

D $(4,1)$

Question 3

Solve by substitution: $y=x+3$ and $2x+y=12$.

A $(6,3)$

B $(3,9)$

C $(3,6)$

D $(4.5,7.5)$

Question 4

Solve by elimination: $x+y=9$ and $x-y=1$.

A $(4,5)$

B $(5,4)$

C $(8,1)$

D $(10,-1)$

Question 5

Which system has no solution?

A $y=3x+1$ and $y=-3x+1$

B $y=3x+1$ and $y=3x-4$

C $y=3x+1$ and $6x-2y=-2$

D $y=3x+1$ and $y=\frac{1}{3}x+1$

Question 6

How many solutions does $y=2x+5$ and $4x-2y=-10$ have?

A No solution

B Exactly one

C Infinitely many

D Exactly two

Question 7

Two numbers have a sum of 20 and a difference of 4. What are the numbers?

The two equations for the numbers.

A 10 and 10

B 16 and 4

C 14 and 6

D 12 and 8

Question 8

Sofia buys 2 sandwiches and 1 juice for $11. Ethan buys 1 sandwich and 1 juice for $7. What does one sandwich cost?

A $3 for a sandwich, $4 for a juice

B $5 for a sandwich, $2 for a juice

C $2 for a sandwich, $5 for a juice

D $4 for a sandwich, $3 for a juice

Question 9

The graphs of two equations cross at $(3,5)$. What does this mean?

The graphs meet at $(3,5)$.

A $x=3$ and $y=5$ make both equations true

B $x=5$ and $y=3$ make both equations true

C $x=3$ and $y=5$ make only one equation true

D The two equations have no solution

Question 10

Which equation can be paired with $2x+y=8$ so the solution is $(3,2)$?

A $x-y=-1$

B $x+y=6$

C $x-y=1$

D $2x-y=3$

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards 8.EE.C.8a, 8.EE.C.8b and 8.EE.C.8c: solve systems of two linear equations in two variables and use them in real-world problems.
The solution of a system is the point where the two graphs intersect.
Substitution replaces one variable with an expression; elimination adds or subtracts equations to cancel a variable.
Parallel lines (same slope, different intercepts) mean no solution; the same line twice means infinitely many.
Always check the ordered pair in both original equations.