To find a point in the solution set of the system of inequalities, we follow these steps:

1. Graph the inequalities:

• $y < \frac{5}{2}x - 3$:
  This is a linear inequality with a slope of $\frac{5}{2}$ and a y-intercept at $(0, -3)$. The region below the line $y = \frac{5}{2}x - 3$ is shaded because $y$ is strictly less than $\frac{5}{2}x - 3$.

• $y \geq -x + 4$:
  This is a linear inequality with a slope of $-1$ and a y-intercept at $(0, 4)$. The region above or on the line $y = -x + 4$ is shaded because $y$ is greater than or equal to $-x + 4$.

2. Identify the solution set:

The solution set is the region where both conditions are satisfied simultaneously.

3. Test a point:

To identify a point in the solution set, choose a point in the overlapping region. For example:

• Consider $(0, 2)$:
  • For $y < \frac{5}{2}x - 3$: Substitute $x = 0, y = 2$: $2 < \frac{5}{2}(0) - 3 \implies 2 < -3 \quad \text{(False)}.$ This point doesn't work; try another point in the region;}Let’s test another point from finding an evaliquant helpful!