1. **State the problem:** Solve the system of linear equations: $$2x + y = 1$$ $$x - 2y = 18$$ 2. **Formula and rules:** We can solve this system using substitution or elimination. Here, we'll use substitution. 3. **Isolate one variable:** From the first equation, isolate $y$: $$y = 1 - 2x$$ 4. **Substitute into second equation:** Substitute $y = 1 - 2x$ into the second equation: $$x - 2(1 - 2x) = 18$$ 5. **Simplify:** $$x - 2 + 4x = 18$$ $$5x - 2 = 18$$ 6. **Solve for $x$:** $$5x = 18 + 2$$ $$5x = 20$$ $$x = \frac{20}{5}$$ $$x = 4$$ 7. **Substitute $x$ back to find $y$:** $$y = 1 - 2(4)$$ $$y = 1 - 8$$ $$y = -7$$ 8. **Final answer:** $$\boxed{(x, y) = (4, -7)}$$