Question

the solutions to the inequality ( y leq -x + 1 ) are shaded on the graph. which point is a solution?
( circ (2, 3) )
( circ (3, -2) )
( circ (2, 1) )
( circ (-1, 3) )

Explanation:

Step1: Recall inequality rule

We test each point in $y \leq -x + 1$

Step2: Test (2,3)

Substitute $x=2,y=3$: $3 \leq -2 + 1 \implies 3 \leq -1$ (False)

Step3: Test (3,-2)

Substitute $x=3,y=-2$: $-2 \leq -3 + 1 \implies -2 \leq -2$ (True)

Step4: Test (2,1)

Substitute $x=2,y=1$: $1 \leq -2 + 1 \implies 1 \leq -1$ (False)

Step5: Test (-1,3)

Substitute $x=-1,y=3$: $3 \leq 1 + 1 \implies 3 \leq 2$ (False)

Answer:

(3, -2)