1. **State the problem:** Solve the system of equations by graphing: $$\begin{cases} y = 2x - 1 \\ y = -x + 5 \end{cases}$$ 2. **Set the equations equal to find the intersection point:** $$2x - 1 = -x + 5$$ 3. **Solve for $x$:** $$2x - 1 = -x + 5$$ $$2x + x = 5 + 1$$ $$3x = 6$$ $$x = \frac{\cancel{3}x}{\cancel{3}} = \frac{6}{3} = 2$$ 4. **Substitute $x=2$ into one of the original equations to find $y$:** $$y = 2(2) - 1 = 4 - 1 = 3$$ 5. **Solution:** The lines intersect at the point $\boxed{(2, 3)}$. This means the solution to the system is $x=2$, $y=3$.