To determine if the point \((-10, 8)\) is a solution to the system of inequalities, we need to substitute \(x = -10\) and \(y = 8\) into each inequality and check if they hold true.
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First Inequality:
\[ y < \frac{1}{10}x + 9 \]
Substitute \(x = -10\) and \(y = 8\): \[ 8 < \frac{1}{10}(-10) + 9 \] Simplifying the right side: \[ 8 < -1 + 9 \] \[ 8 < 8 \] This is not true. -
Second Inequality:
\[ y \geq -\frac{1}{5}x + 5 \]
Substitute \(x = -10\) and \(y = 8\): \[ 8 \geq -\frac{1}{5}(-10) + 5 \] Simplifying the right side: \[ 8 \geq 2 + 5 \] \[ 8 \geq 7 \] This is true.
Since the first inequality is not satisfied, the point \((-10, 8)\) is not a solution to the system of inequalities.