1. **State the problem:** We need to find the graph that represents the solution to the system of inequalities: $$x + y < 4$$ $$2x - 3y \geq 12$$ 2. **Rewrite each inequality and understand shading:** - For $$x + y < 4$$, the boundary line is $$x + y = 4$$. The inequality $$x + y < 4$$ means the region below this line is shaded. - For $$2x - 3y \geq 12$$, the boundary line is $$2x - 3y = 12$$. The inequality $$2x - 3y \geq 12$$ means the region above this line is shaded. 3. **Analyze each graph option:** - **Option A:** Line $$x + y = 4$$ shaded below, and line $$2x - 3y = 12$$ shaded above. This matches the inequalities. - **Option B:** Both lines shaded below, which contradicts $$2x - 3y \geq 12$$. - **Option C:** Both lines shaded above, which contradicts $$x + y < 4$$. - **Option D:** $$x + y = 4$$ shaded above and $$2x - 3y = 12$$ shaded below, both opposite to the inequalities. 4. **Conclusion:** The correct graph is **Option A** because it correctly shows the region below $$x + y = 4$$ and above $$2x - 3y = 12$$. Final answer: **A**