To determine which system of linear inequalities represents the shaded region in the graph, we need to analyze each inequality based on the boundary lines and the direction of shading.

Step 1: Analyzing the Boundary Lines

From the graph, there are two boundary lines:

1. The line with a slope of $\frac{3}{5}$ and a y-intercept of $3$, given by: $y = \frac{3}{5}x + 3$
2. The line with a slope of $\frac{2}{5}$ and a y-intercept of $3$, given by: $y = \frac{2}{5}x + 3$

Step 2: Determining the Inequalities

Looking at the shaded region:

• The shading is below the line $y = \frac{3}{5}x + 3$, indicating $y \leq \frac{3}{5}x + 3$.
• The shading is above the line $y = \frac{2}{5}x + 3$, indicating $y \geq \frac{2}{5}x + 3$.

Conclusion

The system of inequalities that corresponds to the shaded region is: