a system of linear equations y= 2x+5 and y=x+2 which ordered pair is a solution to the equations?

To determine which ordered pair is a solution to the system of linear equations given by \(y = 2x + 5\) and \(y = x + 2\), we need to check each ordered pair and see if both equations are satisfied.

1. **For \( (-3, -1) \)**:
- Substitute \(x = -3\) into \(y = 2x + 5\):
\[
y = 2(-3) + 5 = -6 + 5 = -1 \quad \text{(True)}
\]
- Substitute \(x = -3\) into \(y = x + 2\):
\[
y = -3 + 2 = -1 \quad \text{(True)}
\]
- Both equations are satisfied.

2. **For \( (2, 9) \)**:
- Substitute \(x = 2\) into \(y = 2x + 5\):
\[
y = 2(2) + 5 = 4 + 5 = 9 \quad \text{(True)}
\]
- Substitute \(x = 2\) into \(y = x + 2\):
\[
y = 2 + 2 = 4 \quad \text{(False)}
\]
- Only the first equation is satisfied.

3. **For \( (3, 1) \)**:
- Substitute \(x = 3\) into \(y = 2x + 5\):
\[
y = 2(3) + 5 = 6 + 5 = 11 \quad \text{(False)}
\]
- No need to check the second equation since the first is already false.

4. **For \( (4, 6) \)**:
- Substitute \(x = 4\) into \(y = 2x + 5\):
\[
y = 2(4) + 5 = 8 + 5 = 13 \quad \text{(False)}
\]
- No need to check the second equation since the first is already false.

Therefore, the only ordered pair that is a solution to both equations is:

**a. (-3, -1)**.