1. **State the problem:** Solve the system of equations: $$\begin{cases} y = x - 4 \\ y = 4x + 2 \end{cases}$$ 2. **Use substitution method:** Since both equations equal $y$, set them equal to each other: $$x - 4 = 4x + 2$$ 3. **Solve for $x$:** $$x - 4 = 4x + 2$$ Subtract $4x$ from both sides: $$x - \cancel{4x} - 4 = \cancel{4x} + 2 - 4x \Rightarrow x - 4x - 4 = 2$$ Simplify: $$-3x - 4 = 2$$ Add 4 to both sides: $$-3x - 4 + 4 = 2 + 4 \Rightarrow -3x = 6$$ Divide both sides by $-3$: $$\frac{-3x}{\cancel{-3}} = \frac{6}{\cancel{-3}} \Rightarrow x = -2$$ 4. **Find $y$ by substituting $x = -2$ into one of the original equations:** Using $y = x - 4$: $$y = -2 - 4 = -6$$ 5. **Final answer:** $$x = -2, \quad y = -6$$