To determine if the point (7, –4) is a solution to the system of inequalities, we need to substitute \( x = 7 \) and \( y = -4 \) into each inequality and check if the inequalities hold true.
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First Inequality: \[ y \leq \frac{1}{7}x - 5 \] Substitute \( x = 7 \): \[ -4 \leq \frac{1}{7}(7) - 5 \] This simplifies to: \[ -4 \leq 1 - 5 \] \[ -4 \leq -4 \] This is true.
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Second Inequality: \[ y \leq -\frac{1}{7}x - 3 \] Substitute \( x = 7 \): \[ -4 \leq -\frac{1}{7}(7) - 3 \] This simplifies to: \[ -4 \leq -1 - 3 \] \[ -4 \leq -4 \] This is also true.
Since the point (7, -4) satisfies both inequalities, it is indeed a solution to the system of inequalities.