1. **State the problem:** Graph the system of equations: $$x + 3y = 12$$ $$x = y - 8$$ 2. **Rewrite the equations in slope-intercept form:** From the first equation: $$x + 3y = 12 \implies 3y = 12 - x \implies y = \frac{12 - x}{3} = 4 - \frac{x}{3}$$ From the second equation: $$x = y - 8 \implies y = x + 8$$ 3. **Plot the lines:** - For $$y = 4 - \frac{x}{3}$$, when $$x=0$$, $$y=4$$; when $$x=6$$, $$y=4 - 2 = 2$$. - For $$y = x + 8$$, when $$x=0$$, $$y=8$$; when $$x=-3$$, $$y=5$$. 4. **Identify the intersection point:** From previous calculations, the lines intersect at $$(-3, 5)$$. 5. **Graph description:** - The first line slopes downward with slope $$-\frac{1}{3}$$ and y-intercept 4. - The second line slopes upward with slope 1 and y-intercept 8. 6. **Final conclusion:** The graph shows two lines intersecting at the point $$(-3, 5)$$, confirming the unique solution to the system.