Question

Which ordered pair makes both inequalities true?

y < –x + 1

y > x

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





(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)

Answer 1

Test each point in y < −x + 1 and y > x.

(-3, 5): 5 > −3 (true), 5 < −(−3)+1 = 4 (false) → no.
(-2, 2): 2 > −2 (true), 2 < −(−2)+1 = 3 (true) → yes.
(-1, −3): −3 > −1 (false) → no.
(0, −1): −1 > 0 (false) → no.

Answer: (−2, 2).