Question

Which ordered pair makes both inequalities true?

y < –x + 1

y > x

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.





(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)

Answer 1

To determine which ordered pair makes both inequalities true, we need to test each given pair in the inequalities:

1. **First inequality**: \( y < -x + 1 \)
2. **Second inequality**: \( y > x \)

Let's test each pair:

1. **For (–3, 5)**:
- First inequality: \( 5 < -(-3) + 1 \) ⇒ \( 5 < 3 \) (False)
- Second inequality: \( 5 > -3 \) (True)

2. **For (–2, 2)**:
- First inequality: \( 2 < -(-2) + 1 \) ⇒ \( 2 < 3 \) (True)
- Second inequality: \( 2 > -2 \) (True)

3. **For (–1, –3)**:
- First inequality: \( -3 < -(-1) + 1 \) ⇒ \( -3 < 2 \) (True)
- Second inequality: \( -3 > -1 \) (False)

4. **For (0, –1)**:
- First inequality: \( -1 < -0 + 1 \) ⇒ \( -1 < 1 \) (True)
- Second inequality: \( -1 > 0 \) (False)

After testing all pairs, we see that:

- Only the ordered pair **(–2, 2)** satisfies both inequalities as it is true for both conditions:

1. **For (–2, 2)**:
- \( 2 < 3 \) (True)
- \( 2 > -2 \) (True)

Thus, the ordered pair that makes both inequalities true is **(–2, 2)**.