To determine if the point (4, 10) is a solution to the system of inequalities, we need to check it against each inequality.
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Check the first inequality: \( y \leq 10 \)
For the point (4, 10), \( y = 10 \).
Substituting into the inequality: \[ 10 \leq 10 \] This is true.
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Check the second inequality: \( y > x + 6 \)
Again for the point (4, 10), \( y = 10 \) and \( x = 4 \).
Substituting into the inequality: \[ 10 > 4 + 6 \] This simplifies to: \[ 10 > 10 \] This is false (10 is not greater than 10).
Since the point (4, 10) satisfies the first inequality but not the second, it is not a solution to the system of inequalities.
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