The ordered pair which makes both inequalities true is (-2, 2).
It is given that inequalities are
y < -x + 1 and y > x
For y < -x + 1
Substituting every ordered pair,
1) (-3, 5)
⇒ 5 < - (-3) + 1
⇒ 5 < 3 + 1
⇒ 5 < 4 is false
2) (-2, 2)
⇒ 2 < -(-2) + 1
⇒ 2 < 2 + 1
⇒ 2 < 3 is true
3) (-1, -3)
⇒ -3 < - (-1) + 1
⇒ -3 < 1 + 1
⇒ -3 < 2 is true
4) (0, -1)
⇒ -1 < -0 + 1
⇒ -1 < 1 is true
Now , for y > x
1) (-3, 5)
⇒ 5 > -3 is true
2) (-2, 2)
⇒ 2 > -2 is true
3) (-1, -3)
⇒ -3 > -1 is false
4) (0, -1)
⇒ -1 > 0 is false
Therefore ,the ordered pair which makes both inequalities true is (-2, 2).
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