To determine if the point \((-4, 10)\) is a solution to the given system of inequalities, we need to check whether it satisfies each inequality.
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First Inequality: \[ y \geq -\frac{1}{4}x + 9 \] Substitute \(x = -4\) and \(y = 10\): \[ 10 \geq -\frac{1}{4}(-4) + 9 \] Calculate the right side: \[ -\frac{1}{4}(-4) = 1 \quad \Rightarrow \quad 1 + 9 = 10 \] So the inequality becomes: \[ 10 \geq 10 \] This is true.
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Second Inequality: \[ y < -\frac{1}{2}x + 9 \] Substitute \(x = -4\) and \(y = 10\): \[ 10 < -\frac{1}{2}(-4) + 9 \] Calculate the right side: \[ -\frac{1}{2}(-4) = 2 \quad \Rightarrow \quad 2 + 9 = 11 \] So the inequality becomes: \[ 10 < 11 \] This is true.
Since the point \((-4, 10)\) satisfies both inequalities, it is indeed a solution to the system.
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