1. **State the problem:** Find the intersection point of the two lines given by the equations $y = x - 1$ and $y = 2x - 7$. 2. **Set the equations equal to find the intersection:** Since both expressions equal $y$, set them equal to each other: $$x - 1 = 2x - 7$$ 3. **Solve for $x$:** $$x - 1 = 2x - 7$$ Subtract $x$ from both sides: $$\cancel{x} - 1 = \cancel{x} + 2x - 7 \Rightarrow -1 = x - 7$$ Add 7 to both sides: $$-1 + 7 = x - 7 + 7 \Rightarrow 6 = x$$ 4. **Find $y$ by substituting $x=6$ into one of the original equations:** Using $y = x - 1$: $$y = 6 - 1 = 5$$ 5. **Conclusion:** The lines intersect at the point $(6, 5)$. This means the solution to the system is $x=6$, $y=5$.