Question

Which ordered pair makes both inequalities true? y < -x + 1 and y > x?

A) (-3, 5)
B) (-2, 2)
C) (-1, -3)
D) (0, -1)

Answer 1

The ordered pair (-2, 2) makes both inequalities true.

Step-by-step explanation:

To find the ordered pair that makes both inequalities true, we need to find a point that satisfies both y < -x + 1 and y > x. Let's check each option and substitute the x and y values into the inequalities:

For (-3, 5): 5 < -(-3) + 1 is true, but 5 > -3 is false. So, this option doesn't work.

For (-2, 2): 2 < -(-2) + 1 is true, and 2 > -2 is true. This option satisfies both inequalities.

For (-1, -3): -3 < -(-1) + 1 is false, so this option doesn't work.

For (0, -1): -1 < -(0) + 1 is true, and -1 > 0 is false. So, this option doesn't work.

The ordered pair (-2, 2) is the only one that makes both inequalities true.