Systems of Inequalities Test – Algebra 1 Math (Printable PDF)

Question 1 Test points (2 points)

Decide whether each point is a solution of y < 3x − 4. (a) (4, 7) (1 point) (b) (2, 2) (1 point)

Question 2 Graph an inequality (2 points)

Graph y ≤ 23x − 1 on the grid.

Question 3 Write the inequality (2 points)

Write the inequality for the graph.

Question 4 Solve for y (3 points)

Consider 6x − 3y > 9. (a) Rewrite it with y alone. (1 point) (b) Is the boundary solid or dashed? (1 point) (c) Is (0, 0) in the solution set? (1 point)

Question 5 Read a system (3 points)

Study the shaded solution region of a system of two inequalities.

(a) Write the two inequalities. (2 points) (b) Show that the point (0.5, 2.5) is a solution. (1 point)

Question 6 Choir trip (3 points)

A choir trip has at most 50 seats. Adult tickets cost $20 and student tickets cost $12, and the budget is at most $800. (a) Write a system. (1 point) (b) Is (30, 20) feasible (adults, students)? (1 point) (c) Is (25, 25) feasible? (1 point)

Question 7 Jewelry table (3 points)

Lena makes bracelets b and necklaces n. She wants at least 10 pieces in total and at most 6 necklaces. (a) Write the constraints, including that counts cannot be negative. (1 point) (b) Which of (4, 6), (3, 6) and (5, 4) are feasible? (1 point) (c) Give one more feasible point. (1 point)

Question 8 No solution (2 points)

Explain why the system y > 4x + 9 and y < 4x − 2 has no solution.