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.
a. Yes, because both of these inequalities include points on the line as a solution
b. No, it is not in the solution set for either inequality
c. Yes, it is within the solution set for both inequalities
d. No, it is in the solution set for y<=6x-3, but on the line for 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 check if the point satisfies both inequalities.
For the first inequality y>x+5, we substitute the x and y values of the point (3,8):
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.
For the second inequality y<=6x-3, we substitute the x and y values of the point (3,8):
8 <= 6(3) - 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 d. No, it is in the solution set for y<=6x-3, but on the line for y>x+5.