Question

Which ordered pairs are in the solution set of the system of linear inequalities?

y > Negative one-halfx

y < One-halfx + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 0) and (4, negative 2). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 2, 0) and (2, 2). Everything below the line is shaded.
(5, –2), (3, 1), (–4, 2)
(5, –2), (3, –1), (4, –3)
(5, –2), (3, 1), (4, 2)

Answer 1

Check each point in y > -1/2 x and y < 1/2 x + 1.

(5, -2): -1/2(5) = -2.5, -2 > -2.5 ✓; 1/2(5)+1 = 3.5, -2 < 3.5 ✓. OK.
(3, 1): -1/2(3) = -1.5, 1 > -1.5 ✓; 1/2(3)+1 = 2.5, 1 < 2.5 ✓. OK.
(-4, 2): -1/2(-4) = 2, 2 > 2 is false (it's equal) → not allowed.
(3, -1): -1/2(3) = -1.5, -1 > -1.5 ✓; -1 < 2.5 ✓. OK but not in the same choice with only valid points.
(4, -3): -1/2(4) = -2, -3 > -2 is false → not allowed.
(4, 2): -1/2(4) = -2, 2 > -2 ✓; 1/2(4)+1 = 3, 2 < 3 ✓. OK.

Thus the correct set is (5, -2), (3, 1), (4, 2).