Systems of Linear Equations: Grade 8 Math Test – PDF Download

Question 1: Check an ordered pair (2 points)

Determine whether \((3,-1)\) is a solution of the system \(2x+y=5\) and \(x-y=5\). Show your work.

Question 2: Read a graph (3 points)

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

1. Write the solution shown by the graph. (1 point)
2. Show that it satisfies both equations. (2 points)

Question 3: Solve by graphing (2 points)

Graph \(y=x+1\) and \(y=-2x+7\) on the grid. State the solution of the system.

Question 4: Substitution (2 points)

Solve the system: \(y=4x-5\) and \(2x+y=7\).

Question 5: Elimination (2 points)

Solve the system: \(3x+4y=18\) and \(3x-2y=0\).

Question 6: Multiply both equations (3 points)

Solve the system: \(3x+2y=8\) and \(2x+5y=-2\).

Question 7: How many solutions? (2 points)

Tell how many solutions each system has. Give a reason.

1. \(2x-y=4\) and \(y=2x+3\) (1 point)
2. \(4x+2y=6\) and \(y=-2x+3\) (1 point)

Question 8: School store (2 points)

Diego buys 3 notebooks and 4 pens for $11.50. Aisha buys 3 notebooks and 2 pens for $9.50. Find the price of one notebook and one pen.

Question 9: Gym memberships (2 points)

Gym A charges $45 to join plus $25 per month. Gym B charges $75 to join plus $20 per month. The graph shows the total cost. After how many months do the two gyms cost the same, and what is that cost?

⬇ Download the Grade 8 Systems of Linear Equations test (PDF, 86 KB)

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