Systems of Linear Equations Test – Algebra 1 Math (Printable PDF)

Question 1 Is it a solution? (2 points)

Is (4, −3) a solution of the system 2x + y = 5 and x − 3y = 13? Show your check.

Question 2 Substitution (2 points)

Solve by substitution: y = 3x − 2 and 4x + y = 12.

Question 3 Elimination (2 points)

Solve by elimination: 5x + 4y = 7 and 3x − 4y = 17.

Question 4 Elimination with scaling (3 points)

Solve: 2x + 3y = 19 and 5x − 4y = 13.

Question 5 Number of solutions (2 points)

State how many solutions each system has and justify. (a) y = −3x + 6 and 6x + 2y = 12 (1 point) (b) y = 4x + 2 and y = 4x − 7 (1 point)

Question 6 Solution from a graph (3 points)

A graph of two functions appears below.

(a) Name the point where the graphs meet. (1 point) (b) Verify it in both equations. (1 point) (c) For which input do the two functions have equal outputs, and what is that output? (1 point)

Question 7 Concession stand (3 points)

At a concession stand, 3 hot dogs and 2 sodas cost $15.00, and 2 hot dogs and 3 sodas cost $13.75. (a) Write a system of equations. (1 point) (b) Find the price of a hot dog and of a soda. (1 point) (c) Find the cost of one hot dog and one soda. (1 point)

Question 8 Comparing plans (3 points)

Cost lines for two kayak rental plans are graphed below.

(a) Write one equation that is true when the two plans cost the same. (1 point) (b) Solve it. (1 point) (c) Which plan is cheaper for 6 hours? (1 point)