which ordered pairs make both inequalities true? check all that apply. (-5,5) (0,3) (0,-2) (1,1) (3,-4)

Explanation:

Step 1: Determine inequalities from the graph

Blue dashed line (shaded above): ( y > x + 1 )
Red solid line (shaded below): ( y \leq -x - 1 )

Step 2: Check ((-5, 5))

Substitute into both inequalities:
( 5 > -5 + 1 \rightarrow 5 > -4 ) (true), ( 5 \leq -(-5) - 1 \rightarrow 5 \leq 4 ) (false).

Step 3: Check ((0, 3))

( 3 > 0 + 1 \rightarrow 3 > 1 ) (true), ( 3 \leq -0 - 1 \rightarrow 3 \leq -1 ) (false).

Step 4: Check ((0, -2))

( -2 > 0 + 1 \rightarrow -2 > 1 ) (false), no need to check second inequality.

Step 5: Check ((1, 1))

( 1 > 1 + 1 \rightarrow 1 > 2 ) (false), no need to check second inequality.

Step 6: Check ((3, -4))

( -4 > 3 + 1 \rightarrow -4 > 4 ) (false), no need to check second inequality.

Answer:

None of the ordered pairs make both inequalities true.