Two Variable Inequalities Worksheet
Explore and graph two-variable linear inequalities. This worksheet covers identifying solutions, graphing inequalities, and writing inequalities from graphs.
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Two Variable Inequalities
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Read each question carefully and follow the instructions. Show all your work for graphing problems.
1. Which ordered pair is a solution to the inequality 2x + 3y > 12?
(1, 3)
(3, 2)
(4, 2)
(2, 1)
2. Which ordered pair is NOT a solution to the inequality y < -x + 5?
(0, 4)
(2, 3)
(5, 0)
(3, 1)
3. Graph the inequality y ≥ 2x - 1 on the coordinate plane below.
4. Graph the inequality 3x - y < 6 on the coordinate plane below.
5. Write the inequality represented by the graph below (dashed line through (0, 4) and (4, 0), shaded below).
y x +
6. Write the inequality represented by the graph below (solid line through (0, -2) and (2, 2), shaded above).
y x
7. The graph of y ≤ 2x + 1 will have a dashed boundary line.
True
False
8. The point (0, 0) is a solution to the inequality y > 3x - 2.
True
False
9. A student is selling t-shirts and hats to raise money for a school trip. Each t-shirt costs $15 and each hat costs $10. She needs to raise at least $150. Write an inequality that represents the number of t-shirts (x) and hats (y) she needs to sell.
10. If the student sells 8 t-shirts, how many hats must she sell to reach her goal? Use the inequality from question 9.