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.
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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.
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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.
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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.
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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).