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.