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

Answer:

(3,0) makes the both inequalities true.

Answer 2

The ordered pair that makes both inequalities true is (5/3, -1/3)

Given the system of inequalities

y > –2x + 3

y < x – 2

Equating both expression will give:

-2x + 3 = x - 2

-2x - x  = -2 - 3

-3x = -5

x = 5/3

Since y = x  - 2

y = 5/3 - 2

y = -1/3

Hence the ordered pair that makes both inequalities true is (5/3, -1/3)

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