Question

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

Explanation:

Step1: Test (0,0) in inequalities

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

Step2: Test (0,-1) in inequalities

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

Step3: Test (1,1) in inequalities

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

Step4: Test (3,0) in inequalities

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

Answer:

(3,0)