1. **State the problem:** Solve the system of equations by substitution: $$y = -4x$$ $$y = x + 5$$ 2. **Use substitution method:** Since both expressions equal $y$, set them equal to each other: $$-4x = x + 5$$ 3. **Solve for $x$:** Add $4x$ to both sides: $$\cancel{-4x} + 4x = x + 4x + 5$$ $$0 = 5x + 5$$ Subtract 5 from both sides: $$-5 = 5x$$ Divide both sides by 5: $$\frac{-5}{\cancel{5}} = \frac{5x}{\cancel{5}}$$ $$-1 = x$$ 4. **Find $y$:** Substitute $x = -1$ into one of the original equations, for example $y = x + 5$: $$y = -1 + 5 = 4$$ 5. **Solution:** The solution to the system is: $$(x, y) = (-1, 4)$$