Question

Which ordered pair makes both inequalities true?

y < 3x – 1

y > –x + 4

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

Answer 1

Test each point in both inequalities.

For (4, 0):
- y < 3x − 1 → 0 < 12 − 1 → 0 < 11 (true)
- y > −x + 4 → 0 > −4 + 4 → 0 > 0 (false)

For (1, 2):
- y < 3x − 1 → 2 < 3 − 1 → 2 < 2 (false)
- y > −x + 4 → 2 > −1 + 4 → 2 > 3 (false)

Neither ordered pair satisfies both inequalities.