1. **State the problem:** Solve the system of equations: $$x + y = 10$$ $$x + y = -6$$ 2. **Analyze the system:** Both equations have the same left side $x + y$ but different right sides (10 and -6). 3. **Check for consistency:** Since $x + y$ cannot be both 10 and -6 simultaneously, the system has no solution. 4. **Conclusion:** The system is inconsistent and there is no pair $(x,y)$ that satisfies both equations at the same time.