Question

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

Explanation:

Step1: Test (4,0) in both inequalities

First inequality: $0 < 3(4)-1 \implies 0 < 11$ (True)
Second inequality: $0 \geq -(4)+4 \implies 0 \geq 0$ (True)

Step2: Test (1,2) in both inequalities

First inequality: $2 < 3(1)-1 \implies 2 < 2$ (False)

Step3: Test (0,4) in both inequalities

First inequality: $4 < 3(0)-1 \implies 4 < -1$ (False)

Step4: Test (2,1) in both inequalities

First inequality: $1 < 3(2)-1 \implies 1 < 5$ (True)
Second inequality: $1 \geq -(2)+4 \implies 1 \geq 2$ (False)

Answer:

A. (4,0)