To determine if the point \((-5, 1)\) is a solution to the system of equations given by \(y = 1\) and \(y = -2x - 9\), we need to check if this point satisfies both equations.
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Check the first equation: \(y = 1\)
Substitute \(y = 1\): \[ 1 = 1 \] This is true.
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Check the second equation: \(y = -2x - 9\)
Substitute \(x = -5\) and \(y = 1\): \[ 1 = -2(-5) - 9 \] Simplifying the right side: \[ 1 = 10 - 9 \] \[ 1 = 1 \] This is also true.
Since the point \((-5, 1)\) satisfies both equations, it is indeed a solution to the system of equations.