Systems of Linear Equations: math test, Grade 8 – download the PDF

1 Checking solutions / 2 pts

For each pair, decide whether it is a solution of the system. Show your work.

1. \( (2, -1) \) for \( 3x + 2y = 4 \) and \( x - 3y = 5 \)
2. \( (1, 1) \) for \( x + y = 2 \) and \( 2x - y = 3 \)

2 Graphing / 3 pts

Solve \( y = -x + 6 \) and \( y = 2x - 3 \) by graphing. Give a table of values for \( x = 0, 1, 2, 3 \) for each line, draw both lines, and check your answer.

3 Substitution / 3 pts

Solve by substitution: \( x = 2y + 1 \) and \( 3x - 4y = 9 \).

4 Elimination / 3 pts

Solve by elimination: \( 4x + 3y = -2 \) and \( 2x - 5y = -14 \).

5 How many solutions? / 3 pts

Decide how many solutions each system has. Justify with slopes or algebra.

1. \( y = -4x + 3 \) and \( 8x + 2y = 6 \)
2. \( 3x - y = 2 \) and \( 3x - y = 7 \)
3. \( y = 5x - 1 \) and \( y = -5x - 1 \)

6 Word problem: school store / 6 pts

At a school store, 3 shirts and 2 hats cost $62. One shirt and 4 hats cost $54. Find the price of one shirt and of one hat.