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

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

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

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

No, it is in the solution set for y≤6x−3
, but on the line for y>x+5
.

Answer 1

No — it satisfies y ≤ 6x − 3 but not y > x + 5.

Check: for (3,8), y > x + 5 gives 8 > 3 + 5 → 8 > 8 (false), so it is not in that solution set (it's on the boundary line y = x + 5). For y ≤ 6x − 3, 8 ≤ 6(3) − 3 → 8 ≤ 15 (true), so it is in that solution set.