1. **State the problem:** Solve the system of equations: $$y = x - 15$$ $$y = 4x$$ 2. **Set the equations equal to each other:** Since both expressions equal $y$, we can set them equal: $$x - 15 = 4x$$ 3. **Solve for $x$:** Subtract $x$ from both sides: $$\cancel{x} - 15 = 4\cancel{x}$$ $$-15 = 3x$$ Divide both sides by 3: $$\frac{-15}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$-5 = x$$ 4. **Find $y$:** Substitute $x = -5$ into one of the original equations, for example $y = 4x$: $$y = 4(-5) = -20$$ 5. **Final answer:** The solution to the system is: $$\boxed{(x, y) = (-5, -20)}$$