Question

Determine if the 3, 8 is a solution to the simultaneous inequalities y is greater than x + 5 and y is less than or equal to 6x - 3 select the response that gives the correct answer as well as the correct reasoning

Answer 1

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).

1. **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.

2. **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 \(y > x + 5\).**