To determine whether the point (3, 8) is a solution to the simultaneous inequalities \(y > x + 5\) and \(y \leq 6x - 3\), we'll evaluate each inequality separately.
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Check the first inequality: \(y > x + 5\)
- Substitute \(x = 3\) and \(y = 8\): \[ 8 > 3 + 5 \] \[ 8 > 8 \] This is false because \(8\) is not greater than \(8\). Therefore, the point (3, 8) does not satisfy this inequality.
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Check the second inequality: \(y \leq 6x - 3\)
- Substitute \(x = 3\) and \(y = 8\): \[ 8 \leq 6(3) - 3 \] \[ 8 \leq 18 - 3 \] \[ 8 \leq 15 \] This is true.
Since the point (3, 8) satisfies the second inequality but does not satisfy the first inequality, the correct response would be:
No, it is in the solution set for \(y \leq 6x - 3\), but on the line for \(y > x + 5\).