Question

which ordered pair makes both inequalities true?
y > -2x + 3
y ≤ x - 2
(0,0)
(0, -1)
(1,1)
(3,0)

Explanation:

Step1: Test (0,0)

For \( y > -2x + 3 \): \( 0 > -2(0) + 3 \) → \( 0 > 3 \), false.
For \( y \leq x - 2 \): \( 0 \leq 0 - 2 \) → \( 0 \leq -2 \), false.

Step2: Test (0, -1)

For \( y > -2x + 3 \): \( -1 > -2(0) + 3 \) → \( -1 > 3 \), false.
For \( y \leq x - 2 \): \( -1 \leq 0 - 2 \) → \( -1 \leq -2 \), false.

Step3: Test (1, 1)

For \( y > -2x + 3 \): \( 1 > -2(1) + 3 \) → \( 1 > 1 \), false.
For \( y \leq x - 2 \): \( 1 \leq 1 - 2 \) → \( 1 \leq -1 \), false.

Step4: Test (3, 0)

For \( y > -2x + 3 \): \( 0 > -2(3) + 3 \) → \( 0 > -3 \), true.
For \( y \leq x - 2 \): \( 0 \leq 3 - 2 \) → \( 0 \leq 1 \), true.

Answer:

(3,0)