1. The problem is to identify which graph correctly represents the system of inequalities: $$y > -\frac{1}{2}x + 2$$ $$y < \frac{1}{3}x - 1$$ 2. The first inequality is $y > -\frac{1}{2}x + 2$. This means the region above the line $y = -\frac{1}{2}x + 2$ is shaded. 3. The second inequality is $y < \frac{1}{3}x - 1$. This means the region below the line $y = \frac{1}{3}x - 1$ is shaded. 4. Both lines are dashed because the inequalities are strict (greater than and less than, not including equal). 5. The solution to the system is the intersection of the two shaded regions: above the blue line and below the green line. 6. Graph A shows the blue line with negative slope crossing the y-axis at 2, shaded above, and the green line with positive slope crossing the y-axis at -1, shaded below, with the intersection mostly in the first quadrant. 7. Graph B shows the opposite shading: green shaded above the green line and blue shaded below the blue line, which does not match the inequalities. 8. Therefore, the correct graph representing the system is Graph A. Final answer: Graph A