Algebra 1 Systems Equations Test – Free PDF

Contents

This algebra 1 systems equations test checks systems of linear equations in 45 minutes, with 10 questions for a total of 20 points.

This test has ten questions worth 20 points in total and covers systems of linear equations from standards A-REI.C.5, A-REI.C.6, A-REI.D.11 and A-CED.A.3. Show every step, check each solution, and write answers as ordered pairs. You have 45 minutes.

Test information

Grade: Algebra 1
Chapter: Systems of Linear Equations
Common Core: A-REI.C.5, A-REI.C.6, A-REI.D.11, A-CED.A.3
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 2 pts; Question 7: 2 pts; Question 8: 2 pts; Question 9: 2 pts; Question 10: 2 pts)

Algebra 1 Systems Equations Test: questions 1–5

Question 1: Is it a solution? (2 points)

Consider the system $2x+y=7$ and $x-3y=7$.

Determine whether $(4, -1)$ is a solution. (1 point)
Determine whether $(3, 1)$ is a solution. (1 point)

Question 2: Read the solution (2 points)

The graph shows the system $y=-x+4$ and $y=\frac{1}{2}x+1$.

A system of two lines.

State the solution of the system. (1 point)
Show that this solution satisfies both equations. (1 point)

Question 3: Solve by graphing (2 points)

Graph $y=x-1$ and $y=-2x+5$ on the grid. State the solution of the system.

Grid for graphing.

Question 4: Substitution (2 points)

Solve the system $y=4x-7$ and $3x+2y=8$.

Question 5: Opposite coefficients (2 points)

Solve the system $5x+3y=-1$ and $2x-3y=-13$.

Algebra 1 Systems Equations Test: questions 6–10

Question 6: Multiply first (2 points)

Solve the system $3x+2y=10$ and $5x+3y=17$.

Question 7: Count the solutions (2 points)

Determine how many solutions each system has. Justify each answer.

$y=-3x+2$ and $6x+2y=4$ (1 point)
$4x-2y=6$ and $y=2x+5$ (1 point)

Question 8: Explain elimination (2 points)

Noah adds the equations $3x+y=11$ and $2x-y=4$ and gets $5x=15$.

Explain why every solution of the original system must also satisfy $5x=15$. (1 point)
Find the solution of the original system. (1 point)

Question 9: Ticket problem (2 points)

Sofia’s school sold 150 tickets to a concert. Student tickets cost $\$6$ and adult tickets cost $\$10$. Sales were $1,100. How many student tickets and how many adult tickets were sold?

Question 10: Gym memberships (2 points)

Gym A charges a $\$30$ joining fee plus $\$20$ per month. Gym B has no joining fee and charges $\$35$ per month.

Total cost of each gym.

Write an equation for the total cost $C$ after $m$ months at each gym. (1 point)
Find the month when the two total costs are equal, and that cost. (1 point)