To determine if the point \((-5, 10)\) is a solution to the system of inequalities, we need to substitute \(x = -5\) and \(y = 10\) into each inequality and check if they hold true.
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First inequality: \(15x + 4y \geq 15\)
Substituting \(x = -5\) and \(y = 10\):
\[ 15(-5) + 4(10) \geq 15 \] \[ -75 + 40 \geq 15 \] \[ -35 \geq 15 \quad (\text{This is false}) \]
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Second inequality: \(y > 9\)
Substituting \(y = 10\):
\[ 10 > 9 \quad (\text{This is true}) \]
The first inequality is false, so the point \((-5, 10)\) does not satisfy the entire system of inequalities. Therefore, \((-5, 10)\) is not a solution to the system.
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