Determine if the point (3,8) is a solution to the simultaneous inequalities y>x+5 and y≤6x−3

Question

. Select the response that gives the correct answer as well as the correct reasoning.(1 point)
Responses

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

Yes, it is within the solution set for both inequalities
Yes, it is within the solution set for both inequalities

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<6x−3
, but on the line for y is greater than x plus 5

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

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 with \( x = 3 \) and \( y = 8 \).

1. Evaluate the first inequality \( y > x + 5 \): \[ 8 > 3 + 5 \ 8 > 8 \] This is not true. The point (3, 8) does not satisfy the first inequality.

2. Evaluate the second inequality \( y \leq 6x - 3 \): \[ 8 \leq 6(3) - 3 \ 8 \leq 18 - 3 \ 8 \leq 15 \] This is true. The point (3, 8) satisfies the second inequality.

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

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