Question

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

Explanation:

Step1: Check (2, 3)

Substitute \( x = 2 \), \( y = 3 \) into \( y \leq -x + 1 \):
\( 3 \leq -2 + 1 \) → \( 3 \leq -1 \), false.

Step2: Check (3, -2)

Substitute \( x = 3 \), \( y = -2 \) into \( y \leq -x + 1 \):
\( -2 \leq -3 + 1 \) → \( -2 \leq -2 \), true.

Step3: Check (2, 1)

Substitute \( x = 2 \), \( y = 1 \) into \( y \leq -x + 1 \):
\( 1 \leq -2 + 1 \) → \( 1 \leq -1 \), false.

Step4: Check (-1, 3)

Substitute \( x = -1 \), \( y = 3 \) into \( y \leq -x + 1 \):
\( 3 \leq -(-1) + 1 \) → \( 3 \leq 2 \), false.

Answer:

(3, -2)