1. **Problem:** Write a system of inequalities for the graph showing two lines intersecting, shading on the top left side of the line with positive slope and the bottom right side of the line with negative slope. 2. **Step 1: Identify the lines and shading regions.** - The first line has a positive slope and shading is above or on this line, so inequality is $y \geq x$. - The second line has a negative slope and shading is below this line, so inequality is $y < -x - 2$. 3. **Step 2: Write the system of inequalities.** $$\begin{cases} y \geq x \\ y < -x - 2 \end{cases}$$ 4. **Explanation:** - The inequality $y \geq x$ means all points on or above the line $y = x$. - The inequality $y < -x - 2$ means all points strictly below the line $y = -x - 2$. - The graph shades the region where both inequalities hold. **Final answer:** $$\boxed{\begin{cases} y \geq x \\ y < -x - 2 \end{cases}}$$