1. **State the problem:** Solve the system of equations by substitution: $$y = 2x - 13$$ $$y = x - 5$$ 2. **Use substitution method:** Since both equations equal $y$, set them equal to each other: $$2x - 13 = x - 5$$ 3. **Solve for $x$:** $$2x - 13 = x - 5$$ $$2x - \cancel{x} - 13 = \cancel{x} - 5$$ $$x - 13 = -5$$ $$x = -5 + 13$$ $$x = 8$$ 4. **Substitute $x=8$ back into one of the original equations to find $y$:** Using $y = x - 5$: $$y = 8 - 5$$ $$y = 3$$ 5. **Final solution:** $$\boxed{(x, y) = (8, 3)}$$ This means the two lines intersect at the point $(8, 3)$.