Question

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

y≤x+2


y+x≥4


(1 point)
Responses

(1, 3)
(1, 3)

(2, 6)
(2, 6)

(2, 1)
(2, 1)

(4, -2)

Answer 1

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

1. **First inequality:** \(y \leq x + 2\)
2. **Second inequality:** \(y + x \geq 4\)

Now we will evaluate each option:

1. **For (1, 3):**
- \(y \leq x + 2\)
- \(3 \leq 1 + 2\) (3 ≤ 3) → True
- \(y + x \geq 4\)
- \(3 + 1 \geq 4\) (4 ≥ 4) → True
- This pair is a solution.

2. **For (2, 6):**
- \(y \leq x + 2\)
- \(6 \leq 2 + 2\) (6 ≤ 4) → False
- This pair is not a solution.

3. **For (2, 1):**
- \(y \leq x + 2\)
- \(1 \leq 2 + 2\) (1 ≤ 4) → True
- \(y + x \geq 4\)
- \(1 + 2 \geq 4\) (3 ≥ 4) → False
- This pair is not a solution.

4. **For (4, -2):**
- \(y \leq x + 2\)
- \(-2 \leq 4 + 2\) (-2 ≤ 6) → True
- \(y + x \geq 4\)
- \(-2 + 4 \geq 4\) (2 ≥ 4) → False
- This pair is not a solution.

The only ordered pair that satisfies both inequalities is **(1, 3)**.