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) No, it is not in the solution set for either inequality Yes, because both of these inequalities include points on the line as a solution 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
Are you sure
Yes, I am sure. I have correctly evaluated the inequalities using the given point (3, 8) and provided the correct reasoning. The point (3, 8) satisfies the inequality y <= 6x - 3, but it does not satisfy the inequality y > x + 5.
To determine if the point (3, 8) is a solution to the simultaneous inequalities y > x + 5 and y <= 6x - 3, we need to substitute the values of x and y into both inequalities and check if the inequalities hold true.
First, let's substitute x = 3 and y = 8 into the inequality y > x + 5:
8 > 3 + 5
8 > 8
The inequality is not true, so the point (3, 8) is not in the solution set for y > x + 5.
Next, let's substitute x = 3 and y = 8 into the inequality y <= 6x - 3:
8 <= 6(3) - 3
8 <= 18 - 3
8 <= 15
The inequality is true, so the point (3, 8) is in the solution set for y <= 6x - 3.
Therefore, the correct answer is: No, it is in the solution set for y <= 6x - 3 but on the line for y > x + 5.