To find the ordered pair that is a solution to both equations \( y = 2x + 5 \) and \( y = x + 2 \), we can set the two equations equal to each other since they both equal \( y \).
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Set the equations equal: \[ 2x + 5 = x + 2 \]
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Solve for \( x \): \[ 2x - x = 2 - 5 \] \[ x = -3 \]
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Substitute \( x = -3 \) back into one of the original equations to find \( y \). We can use \( y = x + 2 \): \[ y = -3 + 2 = -1 \]
Thus, the ordered pair that is a solution to both equations is \( (-3, -1) \).
You can also verify this by plugging \( x = -3 \) back into the other equation \( y = 2x + 5 \): \[ y = 2(-3) + 5 = -6 + 5 = -1 \]
Both equations give the same \( y \)-value when \( x = -3 \), confirming the solution is correct.
So the solution is: \[ \text{Ordered pair: } (-3, -1) \]