Question

Which ordered pair makes both inequalities true?

y > –3x + 3

y > 2x – 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 (1, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 3) and (1, 0). Everything to the right of the line is shaded.
(1,0)
(–1,1)
(2,2)

Answer 1

Test each point in both inequalities y > -3x + 3 and y > 2x - 2:

(1,0):
0 > -3(1)+3 = 0 → false
0 > 2(1)-2 = 0 → false

(−1,1):
1 > -3(−1)+3 = 6 → false
1 > 2(−1)-2 = -4 → true

(2,2):
2 > -3(2)+3 = -3 → true
2 > 2(2)-2 = 2 → false (equality, not >)

No given point makes both inequalities true.