1. **State the problem:** We need to graph the system of linear inequalities: $$y \leq -2$$ $$y < 2x - 1$$ 2. **Understand each inequality:** - The first inequality, $y \leq -2$, represents all points on or below the horizontal line $y = -2$. - The second inequality, $y < 2x - 1$, represents all points strictly below the line $y = 2x - 1$. This line is dashed because the inequality is strict (less than, not less than or equal to). 3. **Graph the lines:** - Draw the horizontal line $y = -2$. Since the inequality is $\leq$, this line is solid. - Draw the line $y = 2x - 1$. Since the inequality is $<$, this line is dashed. 4. **Shade the regions:** - For $y \leq -2$, shade the region below and including the line $y = -2$. - For $y < 2x - 1$, shade the region below the dashed line $y = 2x - 1$. 5. **Find the solution region:** - The solution to the system is the intersection of the two shaded regions. - This means the area that is both below or on $y = -2$ and strictly below $y = 2x - 1$. 6. **Interpret the graphs described:** - The first graph shows the dashed line $y = 2x - 1$ with shading below it and a horizontal line at $y = -2$ but no shading below $y = -2$. - The second graph shows the dashed line $y = 2x - 1$ with shading below it and a solid line at $y = -2$ with shading below it. - The third graph shows the dashed line $y = 2x - 1$ with shading below it but shading above $y = -2$, which is incorrect. **Correct graph:** The second graph correctly represents the system because it shows the intersection of the two regions: below $y = 2x - 1$ and below or on $y = -2$. Final answer: The solution region is the area below the dashed line $y = 2x - 1$ and on or below the solid line $y = -2$.