Question

Which ordered pair makes both inequalities true?

y > –2x + 3

y < x – 2

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

Answer 1

Test each point in both inequalities.

For (0,0): 0 > -2(0)+3 → 0 > 3 (false).

For (0,−1): −1 > 3 (false).

For (1,1): 1 > −2(1)+3 → 1 > 1 (false, strict inequality).

For (3,0): 0 > −2(3)+3 → 0 > −3 (true) and 0 < 3−2 → 0 < 1 (true).

So (3,0) is the only point that makes both inequalities true.