Question

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

Explanation:

Step1: Test (1,0) in both inequalities

First inequality: $0 > -3(1)+3 \implies 0 > 0$ (False)
Second inequality: $0 \geq 2(1)-2 \implies 0 \geq 0$ (True)

Step2: Test (-1,1) in both inequalities

First inequality: $1 > -3(-1)+3 \implies 1 > 6$ (False)
Second inequality: $1 \geq 2(-1)-2 \implies 1 \geq -4$ (True)

Step3: Test (2,2) in both inequalities

First inequality: $2 > -3(2)+3 \implies 2 > -3$ (True)
Second inequality: $2 \geq 2(2)-2 \implies 2 \geq 2$ (True)

Step4: Test (0,3) in both inequalities

First inequality: $3 > -3(0)+3 \implies 3 > 3$ (False)
Second inequality: $3 \geq 2(0)-2 \implies 3 \geq -2$ (True)

Answer:

C. (2,2)