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 separately.

1. 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; it is equal to 8.

2. 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 because 8 is less than or equal to 15.

Now, combining the results:

• The point (3, 8) satisfies the second inequality \( y \leq 6x - 3 \) but does not satisfy the first inequality \( y > x + 5 \).

Based on this evaluation:

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