Question

which ordered pair makes both inequalities true?
y < 3x - 1
y ≥ -x + 4
(2, 1)
(0, 4)
(4, 0)

Explanation:

Step1: Test (2,1) in first inequality

Substitute $x=2, y=1$ into $y < 3x - 1$:
$1 < 3(2) - 1$
$1 < 6 - 1$
$1 < 5$ (True)

Step2: Test (2,1) in second inequality

Substitute $x=2, y=1$ into $y \geq -x + 4$:
$1 \geq -2 + 4$
$1 \geq 2$ (False)

Step3: Test (0,4) in first inequality

Substitute $x=0, y=4$ into $y < 3x - 1$:
$4 < 3(0) - 1$
$4 < -1$ (False)

Step4: Test (4,0) in first inequality

Substitute $x=4, y=0$ into $y < 3x - 1$:
$0 < 3(4) - 1$
$0 < 12 - 1$
$0 < 11$ (True)

Step5: Test (4,0) in second inequality

Substitute $x=4, y=0$ into $y \geq -x + 4$:
$0 \geq -4 + 4$
$0 \geq 0$ (True)

Answer:

(4, 0)