Question

y ≤ -x + 1
y > x
options: (-3, 5); (-2, 2); (-1, -3); (0, -1)

Explanation:

Step1: Test point (-3,5) in inequalities

First inequality: $5 \leq -(-3) + 1 \implies 5 \leq 4$ (False)
Second inequality: $5 > -3$ (True)

Step2: Test point (-2,2) in inequalities

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

Step3: Test point (-1,-3) in inequalities

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

Step4: Test point (0,-1) in inequalities

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

Answer:

○ (-2,2)