1. **State the problem:** Solve the first system of equations: $$\begin{cases} x - y = 5 \\ x - y = -2 \end{cases}$$ 2. **Analyze the system:** Both equations have the same left side $x - y$ but different right sides, 5 and -2. 3. **Check for consistency:** Since $x - y$ cannot be both 5 and -2 simultaneously, the system has no solution. 4. **Conclusion:** The first system is inconsistent and has no solution. 1. **State the problem:** Solve the second system of equations: $$\begin{cases} 3x + y = 1 \\ 9x + 3y = 6 \end{cases}$$ 2. **Check if the second equation is a multiple of the first:** Multiply the first equation by 3: $$3 \times (3x + y) = 3 \times 1 \Rightarrow 9x + 3y = 3$$ 3. **Compare with the second equation:** The second equation is $9x + 3y = 6$, which is different from $9x + 3y = 3$. 4. **Interpretation:** The two equations represent parallel lines with no intersection. 5. **Conclusion:** The second system is also inconsistent and has no solution. **Final answer:** Both systems have no solution because they are inconsistent.