1. **State the problem:** Solve the system of equations: $$x - 4y = 8$$ $$2x + y = -2$$ 2. **Choose a method:** We will use substitution or elimination. Here, let's use substitution. 3. **Isolate one variable:** From the first equation, isolate $x$: $$x = 8 + 4y$$ 4. **Substitute into the second equation:** Replace $x$ in the second equation: $$2(8 + 4y) + y = -2$$ 5. **Simplify and solve for $y$:** $$16 + 8y + y = -2$$ $$16 + 9y = -2$$ $$9y = -2 - 16$$ $$9y = -18$$ $$y = \frac{-18}{9}$$ $$y = -2$$ 6. **Substitute $y$ back to find $x$:** $$x = 8 + 4(-2)$$ $$x = 8 - 8$$ $$x = 0$$ 7. **Final answer:** $$\boxed{(x, y) = (0, -2)}$$