To determine if (6, 4) is a solution to the system of equations, we need to substitute \(x = 6\) and \(y = 4\) into both equations and check if they hold true.
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For the first equation: \[ y = 2x - 8 \] Substituting \(x = 6\) and \(y = 4\): \[ 4 = 2(6) - 8 \] \[ 4 = 12 - 8 \] \[ 4 = 4 \quad \text{(True)} \]
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For the second equation: \[ y = -\frac{1}{3}x + 6 \] Substituting \(x = 6\) and \(y = 4\): \[ 4 = -\frac{1}{3}(6) + 6 \] \[ 4 = -2 + 6 \] \[ 4 = 4 \quad \text{(True)} \]
Since (6, 4) satisfies both equations, the answer is yes.