To determine if the point \((-3, -9)\) is a solution to the system of inequalities, we will substitute \(x = -3\) and \(y = -9\) into each inequality and see if the inequalities hold true.
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For the first inequality:
\[ y \leq 6x + 9 \] Substitute \(x = -3\) and \(y = -9\): \[ -9 \leq 6(-3) + 9 \] Calculate the right side: \[ 6(-3) + 9 = -18 + 9 = -9 \] Therefore, we have: \[ -9 \leq -9 \] This inequality is true.
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For the second inequality:
\[ y \leq 5x + 6 \] Substitute \(x = -3\) and \(y = -9\): \[ -9 \leq 5(-3) + 6 \] Calculate the right side: \[ 5(-3) + 6 = -15 + 6 = -9 \] Therefore, we have: \[ -9 \leq -9 \] This inequality is also true.
Since \((-3, -9)\) satisfies both inequalities, it is indeed a solution to the system of inequalities.
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