Determine if the point (3, 8) is a solution to the simultaneous inequalities y > x + 5 and

Question

y ≤ 6x − 3. Select the response that gives the correct answer as well as the correct reasoning.

Answer 1

To determine if the point (3, 8) is a solution to the simultaneous inequalities \( y > x + 5 \) and \( y \leq 6x - 3 \), we will substitute \( x = 3 \) and \( y = 8 \) into each inequality.

1. For the inequality \( y > x + 5 \): \[ 8 > 3 + 5 \] \[ 8 > 8 \] This is not true because \( 8 \) is not greater than \( 8 \). So, the point (3, 8) does not satisfy this inequality.

2. For the inequality \( y \leq 6x - 3 \): \[ 8 \leq 6(3) - 3 \] \[ 8 \leq 18 - 3 \] \[ 8 \leq 15 \] This is true.

Since the point (3, 8) does not satisfy the first inequality \( y > x + 5 \), it is not a solution to the simultaneous inequalities.

Conclusion:

The point (3, 8) is not a solution to the simultaneous inequalities \( y > x + 5 \) and \( y \leq 6x - 3 \) because it fails to satisfy the first inequality.