To determine if the point (2, 10) is a solution to the given system of inequalities, we'll substitute \( x = 2 \) and \( y = 10 \) into each inequality.
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For the first inequality \( y \geq x + 9 \):
Substitute \( x = 2 \) into the inequality:
\[ y \geq 2 + 9 \implies y \geq 11 \]
Now, substituting \( y = 10 \):
\[ 10 \geq 11 \quad \text{(False)} \]
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For the second inequality \( y > 3x + 3 \):
Substitute \( x = 2 \) into the inequality:
\[ y > 3(2) + 3 \implies y > 6 + 3 \implies y > 9 \]
Now, substituting \( y = 10 \):
\[ 10 > 9 \quad \text{(True)} \]
Since (2, 10) does not satisfy the first inequality but does satisfy the second, it is not a solution to the system of inequalities.