1. **State the problem:** Solve the system of linear equations: $$\begin{cases}-4x + y = 6 \\ -5x - y = 21\end{cases}$$ 2. **Add the two equations to eliminate $y$: ** $$(-4x + y) + (-5x - y) = 6 + 21$$ This simplifies to: $$-4x - 5x + y - y = 27$$ $$-9x = 27$$ 3. **Solve for $x$: ** $$x = \frac{27}{-9}$$ $$x = -3$$ 4. **Substitute $x = -3$ into the first equation to find $y$: ** $$-4(-3) + y = 6$$ $$12 + y = 6$$ $$y = 6 - 12$$ $$y = -6$$ 5. **Final answer:** $$\boxed{(x, y) = (-3, -6)}$$