1. **State the problem:** Find the solution to the system of equations: $$y = 2x - 1$$ $$y = -x + 5$$ 2. **Set the equations equal to each other** because both equal $y$: $$2x - 1 = -x + 5$$ 3. **Solve for $x$:** Add $x$ to both sides: $$2x + x - 1 = 5$$ Simplify: $$3x - 1 = 5$$ Add 1 to both sides: $$3x = 6$$ Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{6}{3}$$ $$x = 2$$ 4. **Find $y$ by substituting $x=2$ into one of the original equations:** Using $y = 2x - 1$: $$y = 2(2) - 1 = 4 - 1 = 3$$ 5. **Solution:** The lines intersect at the point $(2, 3)$. 6. **Check the answer against the options:** Option C is $(2, 3)$. **Final answer:** C. (2, 3)