1. **State the problem:** Solve the system of equations: $$y = \frac{1}{2}x + 5$$ $$-2x - 8y = 8$$ 2. **Use substitution method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y = \frac{1}{2}x + 5$ into the second equation. 3. **Substitute and simplify:** $$-2x - 8\left(\frac{1}{2}x + 5\right) = 8$$ $$-2x - 8 \cdot \frac{1}{2}x - 8 \cdot 5 = 8$$ $$-2x - 4x - 40 = 8$$ 4. **Combine like terms:** $$-6x - 40 = 8$$ 5. **Isolate $x$:** $$-6x = 8 + 40$$ $$-6x = 48$$ 6. **Divide both sides by $-6$:** $$x = \frac{48}{\cancel{-6}}\cancel{-1} = -8$$ 7. **Find $y$ by substituting $x = -8$ into the first equation:** $$y = \frac{1}{2}(-8) + 5 = -4 + 5 = 1$$ 8. **Final answer:** The solution to the system is the ordered pair $$\boxed{(-8, 1)}$$.