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)
(0,4)
(2,1)

Answer 1

(4, 0)

Check: for (4,0), y < 3x − 1 gives 0 < 11 (true). The second line is solid so the boundary is included, so y ≥ −x + 4; at (4,0) that is 0 ≥ 0 (true). Thus (4,0) lies in the shaded region.