Question

Which ordered pair is a solution of the following system of linear inequalities.

y≤x+2

y+x≥4

(1 point)
Responses

(2,1)
(2,1)

(1,3)
(1,3)

(4,-2)
(4,-2)

(2,6)

Answer 1

To determine which ordered pair is a solution to the given system of linear inequalities, we will check each pair against both inequalities:

1. **Inequalities:**
- \( y \leq x + 2 \)
- \( y + x \geq 4 \)

2. **Ordered pairs to check:**
- (2, 1)
- (1, 3)
- (4, -2)
- (2, 6)

Let's check each ordered pair:

1. **For (2, 1):**
- Check \( y \leq x + 2 \):
- \( 1 \leq 2 + 2 \) (True)
- Check \( y + x \geq 4 \):
- \( 1 + 2 \geq 4 \) (False)

2. **For (1, 3):**
- Check \( y \leq x + 2 \):
- \( 3 \leq 1 + 2 \) (True)
- Check \( y + x \geq 4 \):
- \( 3 + 1 \geq 4 \) (True)
- Both conditions are satisfied.

3. **For (4, -2):**
- Check \( y \leq x + 2 \):
- \( -2 \leq 4 + 2 \) (True)
- Check \( y + x \geq 4 \):
- \( -2 + 4 \geq 4 \) (True)
- Both conditions are satisfied.

4. **For (2, 6):**
- Check \( y \leq x + 2 \):
- \( 6 \leq 2 + 2 \) (False)

After checking all the pairs, we can conclude that both (1, 3) and (4, -2) are solutions to the system of inequalities.

So, the ordered pair (1, 3) is the first one that satisfies both inequalities.

**Final answer: (1, 3)**