To check if \((-2, -3)\) is a solution to the system of inequalities, we need to substitute \(x = -2\) and \(y = -3\) into each inequality and see if they hold true.
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First Inequality: \(20x - 11y \leq -11\)
Substituting \(x = -2\) and \(y = -3\):
\[ 20(-2) - 11(-3) \leq -11 \]
\[ -40 + 33 \leq -11 \]
\[ -7 \leq -11 \]
This is false.
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Second Inequality: \(2x - 12y > -14\)
Substituting \(x = -2\) and \(y = -3\):
\[ 2(-2) - 12(-3) > -14 \]
\[ -4 + 36 > -14 \]
\[ 32 > -14 \]
This is true.
Since \((-2, -3)\) does not satisfy the first inequality but satisfies the second inequality, it is not a solution to the system of inequalities.
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