Question

A graph with the points (-1, 5), (0.923, 1.6), (5, 2), and (-4, -2)

Which of the points on the graph is a solution for the simultaneous inequalities y > 4x - 2 and y ≥ -1/3 x + 2? Enter the x-value by the y-value

(__, __)

Answer 1

Check each point in both inequalities.

1. (-1, 5): 4(-1)-2 = -6, and 5 > -6 (true). -(1/3)(-1)+2 = 7/3 ≈ 2.333, and 5 ≥ 7/3 (true). → satisfies both.

2. (0.923, 1.6): 4(0.923)-2 = 1.692, but 1.6 > 1.692 is false.

3. (5, 2): 4(5)-2 = 18, but 2 > 18 is false.

4. (-4, -2): -(1/3)(-4)+2 = 10/3 ≈ 3.333, but -2 ≥ 3.333 is false.

Only (-1, 5) satisfies both. Answer: (-1, 5)