1. **Problem Statement:** Determine which system of inequalities corresponds to the shaded solution region shown in the graph. 2. **Given Information:** - One line is solid, representing $y \leq x - 1$ with shading below it. - The other line is dashed, representing $y > \frac{1}{2}x$ with shading above it. - The solution region is where the shading overlaps: above the dashed line and below the solid line. 3. **Understanding the inequalities:** - A solid line means the inequality includes equality ($\leq$ or $\geq$). - A dashed line means strict inequality ($<$ or $>$). - The shading above $y > \frac{1}{2}x$ means all points satisfy $y > \frac{1}{2}x$. - The shading below $y \leq x - 1$ means all points satisfy $y \leq x - 1$. 4. **Conclusion:** The system of inequalities that matches the graph is: $$ y > \frac{1}{2}x \quad \text{and} \quad y \leq x - 1 $$ **Final answer:** The system is $y > \frac{1}{2}x$ and $y \leq x - 1$.