1. **State the problem:** Solve the system of equations by graphing: $$x + y = 2$$ $$y = -\frac{1}{5}x - 2$$ 2. **Rewrite the first equation in slope-intercept form:** $$x + y = 2 \implies y = 2 - x$$ This means the first line has slope $-1$ and y-intercept $2$. 3. **Graph both lines:** - Line 1: $y = 2 - x$ - Line 2: $y = -\frac{1}{5}x - 2$ 4. **Find the intersection point algebraically to confirm the graph:** Set the right sides equal: $$2 - x = -\frac{1}{5}x - 2$$ 5. **Solve for $x$:** $$2 - x = -\frac{1}{5}x - 2$$ Add $\frac{1}{5}x$ to both sides: $$2 - x + \frac{1}{5}x = -2$$ Rewrite $-x + \frac{1}{5}x$ as $-\frac{5}{5}x + \frac{1}{5}x = -\frac{4}{5}x$: $$2 - \frac{4}{5}x = -2$$ Subtract 2 from both sides: $$-\frac{4}{5}x = -2 - 2$$ $$-\frac{4}{5}x = -4$$ 6. **Divide both sides by $-\frac{4}{5}$:** $$x = \frac{-4}{-\frac{4}{5}} = -4 \times \frac{5}{-4} = \cancel{-4} \times \frac{5}{\cancel{-4}} = 5$$ 7. **Find $y$ by substituting $x=5$ into one of the equations:** Using $y = 2 - x$: $$y = 2 - 5 = -3$$ 8. **Solution:** The lines intersect at the point $\boxed{(5, -3)}$. This is the solution to the system of equations by graphing.