1. **State the problem:** We need to solve the system of equations: $$6x - 2y = -6$$ $$11 = y - 5x$$ Tim claims the solution is $x = -9$, $y = -4$, but we need to verify and find the correct solution. 2. **Rewrite the second equation:** $$11 = y - 5x \implies y = 11 + 5x$$ 3. **Substitute $y$ into the first equation:** $$6x - 2(11 + 5x) = -6$$ 4. **Simplify the equation:** $$6x - 22 - 10x = -6$$ 5. **Combine like terms:** $$6x - 10x - 22 = -6$$ $$-4x - 22 = -6$$ 6. **Add 22 to both sides:** $$-4x - 22 + 22 = -6 + 22$$ $$-4x = 16$$ 7. **Divide both sides by $-4$:** $$x = \frac{16}{\cancel{-4}}\cancel{-1} = -4$$ 8. **Substitute $x = -4$ back into $y = 11 + 5x$:** $$y = 11 + 5(-4) = 11 - 20 = -9$$ 9. **Final solution:** $$x = -4, \quad y = -9$$ 10. **Check Tim's solution:** Tim said $x = -9$, $y = -4$, which swaps the values. This is likely the error he made. **Answer:** The correct solution is $x = -4$, $y = -9$. Tim probably swapped the values of $x$ and $y$.