To determine if the point (3, 8) is a solution to the simultaneous inequalities \(y > x + 5\) and \(y \leq 6x - 3\), we need to evaluate each inequality using the coordinates (3, 8).
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Check the first inequality: \[ y > x + 5 \] Substitute \(x = 3\) and \(y = 8\): \[ 8 > 3 + 5 \] Simplifying gives: \[ 8 > 8 \] This statement is false because 8 is not greater than 8.
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Check the second inequality: \[ y \leq 6x - 3 \] Substitute \(x = 3\) and \(y = 8\): \[ 8 \leq 6(3) - 3 \] Simplifying the right side gives: \[ 8 \leq 18 - 3 \] \[ 8 \leq 15 \] This statement is true.
Conclusion:
For the point (3, 8):
- It does not satisfy the first inequality (\(y > x + 5\) is false).
- It satisfies the second inequality (\(y \leq 6x - 3\) is true).
Since the point must satisfy both inequalities to be a solution to the system, (3, 8) is not a solution.
Therefore, the correct response is: (3, 8) is not a solution because it does not satisfy the inequality \(y > x + 5\).
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