1. **State the problem:** Determine the number of solutions for the system of equations: $$\begin{cases} y = -x - 3 \\ -2x - 2y = 6 \end{cases}$$ 2. **Use substitution or elimination:** We can substitute $y$ from the first equation into the second. 3. Substitute $y = -x - 3$ into $-2x - 2y = 6$: $$-2x - 2(-x - 3) = 6$$ 4. Simplify the left side: $$-2x + 2x + 6 = 6$$ 5. Combine like terms: $$\cancel{-2x} + \cancel{2x} + 6 = 6$$ $$6 = 6$$ 6. Since the equation simplifies to a true statement, the system is dependent, meaning the two equations represent the same line. 7. **Conclusion:** There are infinitely many solutions because the two equations describe the same line. **Final answer:** C. Infinite solutions