Question

which ordered pair makes both inequalities true?
y < 3x - 1
y ≥ -x + 4
graph of the system of inequalities

Explanation:

Step1: Test (4,0) in \( y < 3x - 1 \)

Substitute \( x = 4 \), \( y = 0 \): \( 0 < 3(4) - 1 = 11 \), true.
Substitute in \( y \geq -x + 4 \): \( 0 \geq -4 + 4 = 0 \), true.

Step2: Test (1,2) in \( y < 3x - 1 \)

Substitute \( x = 1 \), \( y = 2 \): \( 2 < 3(1) - 1 = 2 \), false.

Step3: Test (0,4) in \( y < 3x - 1 \)

Substitute \( x = 0 \), \( y = 4 \): \( 4 < 3(0) - 1 = -1 \), false.

Answer:

(4,0)