1. The problem is to identify which graph correctly represents the system of inequalities: $$y \leq -3x - 1$$ $$y < \frac{1}{2}x + 5$$ 2. The first inequality, $y \leq -3x - 1$, is represented by a solid line because it includes equality ($\leq$). The region below this line (including the line) is shaded. 3. The second inequality, $y < \frac{1}{2}x + 5$, is represented by a dashed line because it does not include equality ($<$). The region below this dashed line is shaded. 4. The solution to the system is the intersection of the shaded regions: below the solid line and below the dashed line. 5. Graph A shows a solid blue line with slope $-3$ and intercept $-1$, and a dashed green line with slope $\frac{1}{2}$ and intercept $5$. The shaded region is below both lines, matching the system. 6. Graph B shows the dashed green line shading above it, which contradicts $y < \frac{1}{2}x + 5$. Therefore, the correct graph representing the system is Graph A.