To determine if the point \((-6, 6)\) is a solution to the system of equations, we can substitute \(x = -6\) and \(y = 6\) into both equations and see if they hold true.
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First equation:
\(17x + 15y = -12\)Substitute \(x = -6\) and \(y = 6\): \[ 17(-6) + 15(6) = -12 \] Calculate: \[ -102 + 90 = -12 \] \[ -12 = -12 \quad \text{(True)} \]
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Second equation:
\(8x + 5y = -3\)Substitute \(x = -6\) and \(y = 6\): \[ 8(-6) + 5(6) = -3 \] Calculate: \[ -48 + 30 = -3 \] \[ -18 = -3 \quad \text{(False)} \]
Since the second equation does not hold true, \((-6, 6)\) is not a solution to the system of equations.