1. **State the problem:** Solve the system of equations by graphing: $$y = -2x + 8$$ $$y = x + 5$$ 2. **Understand the problem:** We want to find the point(s) where the two lines intersect. This point satisfies both equations simultaneously. 3. **Set the equations equal to each other:** Since both equal $y$, set the right sides equal: $$-2x + 8 = x + 5$$ 4. **Solve for $x$:** $$-2x + 8 = x + 5$$ Add $2x$ to both sides: $$\cancel{-2x} + 8 + 2x = x + 5 + 2x$$ $$8 = 3x + 5$$ Subtract 5 from both sides: $$8 - 5 = 3x + \cancel{5} - 5$$ $$3 = 3x$$ Divide both sides by 3: $$\frac{3}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$1 = x$$ 5. **Find $y$ by substituting $x=1$ into one of the original equations:** Using $y = x + 5$: $$y = 1 + 5 = 6$$ 6. **Solution:** The lines intersect at the point $(1, 6)$. This means the solution to the system is: $$\boxed{(1, 6)}$$