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. No, it is in the solution set for y less-than-or-equal-to 6 x minus 3 , but on the line for y greater than x plus 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.
For the inequality y>x+5:
8 > 3 + 5
8 > 8
This is not true, so the point (3,8) is not a solution to y>x+5.
For the inequality y≤6x−3:
8 ≤ 6(3) - 3
8 ≤ 18 - 3
8 ≤ 15
This is true, so the point (3,8) is a solution to 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.