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, 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. 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.

Answer 1

To determine if the point (3,8) is a solution to the simultaneous inequalities y > x+5 and y ≤ 6x - 3, we can check if the point satisfies both inequalities.

For the inequality y > x+5:
8 > 3+5
8 > 8
This inequality is not true, so the point (3,8) is not in the solution set for y > x+5.

For the inequality y ≤ 6x - 3:
8 ≤ 6(3) - 3
8 ≤ 18 - 3
8 ≤ 15
This inequality is true, so the point (3,8) is in the solution set for y ≤ 6x - 3.

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