Question

Determine if the point (3,8)
is a solution to the simultaneous inequalities y>x+5
and y≤6x−3
. Select the response that gives the correct answer as well as the correct reasoning.(1 point)
Responses

A) No, it is in the solution set for y≤6x−3, but on the line for y>x+5
.
No, it is in the solution set for y less-than-or-equal-to 6 x minus 3 , but on the line for y greater than x plus 5 .

B) No, it is not in the solution set for either inequality.

C) Yes, because both of these inequalities include points on the line as a solution.

D) Yes, it is within the solution set for both inequalities.

Answer 1

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

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

2. **Check the second inequality**: \(y \leq 6x - 3\)
- Substitute \(x = 3\) and \(y = 8\):
\[
8 \leq 6(3) - 3 \implies 8 \leq 18 - 3 \implies 8 \leq 15
\]
This is true.

Since the point (3,8) does not satisfy the first inequality, it cannot be considered a solution to both inequalities.

Therefore, the correct response is:

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