To determine if the point (7, -8) is a solution to the system of inequalities, we need to substitute \(x = 7\) and \(y = -8\) into each inequality and verify if the point satisfies both.
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First Inequality: \(y < \frac{3}{7}x + 7\)
Substitute \(x = 7\) and \(y = -8\):
\[ -8 < \frac{3}{7}(7) + 7 \]
Simplifying the right side:
\[ -8 < 3 + 7 \] \[ -8 < 10 \]
This is true.
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Second Inequality: \(y \geq -x + 10\)
Substitute \(x = 7\) and \(y = -8\):
\[ -8 \geq -7 + 10 \]
Simplifying the right side:
\[ -8 \geq 3 \]
This is false.
Since the point (7, -8) satisfies the first inequality but does not satisfy the second inequality, the point (7, -8) is not a solution to the system of inequalities.