Algebra 1 Systems Equations Quiz – Free PDF

Contents

This algebra 1 systems equations quiz asks 10 multiple-choice questions on systems of linear equations, and each answer comes with a short explanation.

Take this ten-question quiz to check what you know about solving systems of linear equations and reading where graphs meet. Each question has exactly one correct answer. Read the explanation after each choice, especially for the ones you miss.

Algebra 1Common Core: A-REI.C.5 · A-REI.C.6 · A-REI.D.11 · A-CED.A.3

🎯 Systems of Linear Equations – Algebra 1 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

The graph shows two lines. What is the solution of the system?

Two lines in the plane.

A (4, 2)

B (0, 2)

C (3, 5)

D (2, 4)

Question 2

Which ordered pair is the solution of $x+y=7$ and $x-y=1$?

A (4, 3)

B (5, 2)

C (3, 4)

D (6, 1)

Question 3

What is the solution of $y=2x$ and $x+y=12$?

A (8, 4)

B (6, 6)

C (4, 8)

D (3, 6)

Question 4

Which first step eliminates a variable in $2x+3y=7$ and $4x-3y=5$?

A Subtract the equations to eliminate y

B Add the equations to eliminate x

C Subtract the equations to eliminate x

D Add the equations to eliminate y

Question 5

How many solutions does the system in the graph have?

Two lines in the plane.

A Exactly one solution

B Exactly two solutions

C Infinitely many solutions

D No solution

Question 6

How many solutions does the system $y=2x+1$ and $4x-2y=-2$ have?

A Infinitely many solutions

B No solution

C Exactly one solution

D Exactly two solutions

Question 7

A theater sold 40 tickets, some at $\$3$ and the rest at $\$5$, for $\$164$. How many $\$5$ tickets were sold?

A 18

B 22

C 20

D 24

Question 8

Which values of $x$ solve $x^{2}=x+2$, using the graph?

The graphs of two functions.

A x = −1 and x = 2

B x = 1 and x = 4

C x = −2 and x = 1

D x = 1 and x = 2

Question 9

The pair $(3, 2)$ solves $2x+y=8$ and $x-y=1$. Which equation must $(3, 2)$ also solve?

A x = 9

B 3x = 9

C x + 2y = 9

D 3y = 9

Question 10

Bike rental A costs $\$12$ plus $\$4$ per hour. Rental B costs $\$4$ plus $\$6$ per hour. After how many hours do they cost the same?

A 2 hours

B 8 hours

C 4 hours

D 28 hours

🎉 Quiz complete!

0 / 10

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 A-REI.C.5, A-REI.C.6, A-REI.D.11 and A-CED.A.3: solve systems by graphing, substitution and elimination, and model real situations.
Two lines meet once, never, or everywhere: one solution, no solution, or infinitely many.
Substitution works best when a variable is already isolated; elimination works best when coefficients match or are opposites.
Adding equations is valid because equal quantities added to equal quantities stay equal.
The x-coordinates where two graphs meet solve $f(x)=g(x)$ for lines, parabolas and exponentials alike.