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 no, it is not in the solution set for either inequality. 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, because both of these inequalities include points on the line as a solution. 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 . paint

Answer 1

To determine whether the point (3, 8) is a solution to the inequalities \( y > x + 5 \) and \( y \leq 6x - 3 \), we need to evaluate both inequalities.

1. Evaluate the first inequality: \[ y > x + 5 \] Substitute \( x = 3 \) and \( y = 8 \): \[ 8 > 3 + 5 \] \[ 8 > 8 \] This is false since 8 is not greater than 8.

2. Evaluate the second inequality: \[ y \leq 6x - 3 \] Substitute \( x = 3 \) and \( y = 8 \): \[ 8 \leq 6(3) - 3 \] \[ 8 \leq 18 - 3 \] \[ 8 \leq 15 \] This is true.

The point (3, 8) is not in the solution set for \( y > x + 5 \) but it is in the solution set for \( y \leq 6x - 3 \).

Thus, the correct response is: no, it is in the solution set for \( y \leq 6x - 3 \), but on the line for \( y > x + 5 \).