Question

Determine if the point (3, 8) is a solution to the simultaneous inequalities y>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.
No, it is in the solution set for y is less than or equal to 6x-3, but on the line for y is greater than x+5

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 will evaluate each inequality using the point \( (3, 8) \):

1. **Check the first inequality: \(y > x + 5\)**
- Substitute \(x = 3\) and \(y = 8\):
\[
8 > 3 + 5
\]
\[
8 > 8
\]
This is **not true** (since 8 is not greater than 8). Hence, the point does not satisfy this inequality.

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**.

Now, since the point (3, 8) satisfies the second inequality but does not satisfy the first inequality, it does not satisfy both inequalities simultaneously.

Thus, the correct response is:
**No, it is in the solution set for \(y \leq 6x - 3\), but it does not satisfy \(y > x + 5\).**