The problem asks how Stephanie can determine if the point $(3, -4)$ is a solution to the system of inequalities $y < -2x + 3$ and $y > 5x - 3$.

1. Problem Description

The problem asks how Stephanie can determine if the point $(3, -4)$ is a solution to the system of inequalities $y < -2x + 3$ and $y > 5x - 3$.

2. Solution Steps

To determine if a point is a solution to a system of inequalities, substitute the $x$ and $y$ values of the point into each inequality. If the point satisfies all inequalities, it is a solution to the system.

In this case, the point is $(3, -4)$, so $x = 3$ and $y = -4$.

First, substitute these values into $y < -2x + 3$:

$-4 < -2(3) + 3$

$-4 < -6 + 3$

$-4 < -3$

This inequality is true.

Next, substitute the values into $y > 5x - 3$:

$-4 > 5(3) - 3$

$-4 > 15 - 3$

$-4 > 12$

This inequality is false.

Since the point $(3, -4)$ satisfies $y < -2x + 3$ but does not satisfy $y > 5x - 3$, it is not a solution to the system.

The correct method to determine if the point is a solution to the system of inequalities is to substitute the point into each inequality. If the point satisfies both inequalities, it is a solution.

3. Final Answer

A. She could substitute 3 for x and -4 for y in each inequality. If the point satisfies both inequalities, it lies in the region that is a solution. Otherwise, it does not.