To determine if the point \((4, -1)\) is a solution to the system of inequalities, we need to plug in the values \(x = 4\) and \(y = -1\) into both inequalities and see if they hold true.
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For the first inequality: \[ 6x + 17y < 11 \] Substituting \(x\) and \(y\): \[ 6(4) + 17(-1) < 11 \] Calculate: \[ 24 - 17 < 11 \] \[ 7 < 11 \quad \text{(True)} \]
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For the second inequality: \[ 5x + 8y > 17 \] Substituting \(x\) and \(y\): \[ 5(4) + 8(-1) > 17 \] Calculate: \[ 20 - 8 > 17 \] \[ 12 > 17 \quad \text{(False)} \]
Since the first inequality is true, but the second inequality is false, the point \((4, -1)\) is not a solution to the system of inequalities.