1. **State the problem:** Solve the system of equations by graphing: $$y = x - 8$$ $$y = -2x + 1$$ 2. **Formula and rules:** To solve by graphing, plot both lines on the coordinate plane and find their intersection point. 3. **Plot the first line $y = x - 8$:** - When $x=0$, $y=0-8=-8$ (point $(0,-8)$). - When $x=8$, $y=8-8=0$ (point $(8,0)$). 4. **Plot the second line $y = -2x + 1$:** - When $x=0$, $y=1$ (point $(0,1)$). - When $x=1$, $y=-2(1)+1=-2+1=-1$ (point $(1,-1)$). 5. **Find the intersection algebraically:** Set $x - 8 = -2x + 1$ $$x - 8 = -2x + 1$$ $$x + 2x = 1 + 8$$ $$3x = 9$$ $$x = \cancel{\frac{3x}{3}}{\frac{9}{3}} = 3$$ 6. Substitute $x=3$ into $y = x - 8$: $$y = 3 - 8 = -5$$ 7. **Solution:** The lines intersect at the point $(3, -5)$. This is the solution to the system.