Systems of Equations Test – Grade 8 Math (Printable PDF)

Question 1 Read and verify (2 points)

The graph shows y = x − 2 and y = −x + 6. State the solution (1 point) and verify it in both equations (1 point).

Question 2 Substitution (3 points)

Solve by substitution:

y = 4x − 5
2x + y = 13

Question 3 Elimination (3 points)

Solve by elimination:

4x + 3y = 25
2x − 3y = −1

Question 4 Classify the systems (3 points)

Without solving, state the number of solutions of each system. (1 point each)

1. y = 5x − 2 and y = 5x + 7
2. 6x + 3y = 9 and 2x + y = 3
3. y = 4x and y = −x

Question 5 County fair tickets (3 points)

Adult tickets cost $9 and child tickets cost $5. A total of 120 tickets were sold for $860. Write a system (1 point) and find how many of each were sold (2 points).

Question 6 Pool memberships (3 points)

Plan A: $4 fee plus $2 per visit (y = 2x + 4). Plan B: $1 fee plus $3 per visit (y = 3x + 1). The graph shows both.

1. Read the intersection point. (1 point)
2. Explain what it means. (1 point)
3. Which plan is cheaper for 5 visits? (1 point)

Question 7 Is it a solution? (2 points)

Is (−2, 5) a solution of the system 2x + y = 1 and x − y = −7? Show each check. (1 point per equation)

Question 8 Parallel on purpose (1 point)

Write a second equation so that the system with y = 2x + 1 has no solution.