Question

Determine if the point (3, 8) is a solution to the simulation inequalities y > x + 5 and 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 inequalities \( y > x + 5 \) and \( y < 6x - 3 \), we will substitute \( x = 3 \) and \( y = 8 \) into each inequality and check if they hold true.

1. For the first inequality:
\[
y > x + 5
\]

Substituting the values:
\[
8 > 3 + 5
\]
\[
8 > 8
\]

This statement is **false** because 8 is not greater than 8.

2. For the second inequality:
\[
y < 6x - 3
\]

Again substituting:
\[
8 < 6(3) - 3
\]
\[
8 < 18 - 3
\]
\[
8 < 15
\]

This statement is **true**.

Since the point (3, 8) does not satisfy the first inequality, it cannot be a solution to the system of inequalities.

**Correct Answer:** The point (3, 8) is not a solution. The first inequality \( y > x + 5 \) is false at this point.