Determine if the point (3,8)

To determine if the point (3, 8) is a solution to the simultaneous inequalities \( y > x + 5 \) and \( y \leq 6x - 3 \), we will evaluate each inequality with this point.

1. **Check the first inequality: \( y > x + 5 \)**

Plug in \( x = 3 \) and \( y = 8 \):
\[
8 > 3 + 5
\]
\[
8 > 8
\]
This statement is **false** because 8 is not greater than 8. Thus, the point (3, 8) does not satisfy this inequality.

2. **Check the second inequality: \( y \leq 6x - 3 \)**

Again, plug in \( x = 3 \) and \( y = 8 \):
\[
8 \leq 6(3) - 3
\]
\[
8 \leq 18 - 3
\]
\[
8 \leq 15
\]
This statement is **true** because 8 is indeed less than or equal to 15.

Since the point (3, 8) satisfies the second inequality but does not satisfy the first inequality, the appropriate response is:

**No, it is in the solution set for \( y \leq 6x - 3 \), but on the line for \( y > x + 5 \).**