1. **State the problem:** Solve the system of equations by graphing: $$x + 3y = 12$$ $$x = y - 8$$ Determine if the system has one solution, infinitely many solutions, or no solution. 2. **Rewrite the second equation:** To compare easily, express both equations in terms of $y$ or $x$. From the second equation: $$x = y - 8 \implies y = x + 8$$ 3. **Rewrite the first equation in terms of $y$:** $$x + 3y = 12 \implies 3y = 12 - x \implies y = \frac{12 - x}{3}$$ 4. **Set the two expressions for $y$ equal to find intersection:** $$x + 8 = \frac{12 - x}{3}$$ 5. **Multiply both sides by 3 to clear the denominator:** $$3(x + 8) = 12 - x$$ $$3x + 24 = 12 - x$$ 6. **Bring all terms to one side:** $$3x + x = 12 - 24$$ $$4x = -12$$ $$x = \frac{-12}{4}$$ $$x = -3$$ 7. **Find $y$ by substituting $x = -3$ into $y = x + 8$:** $$y = -3 + 8 = 5$$ 8. **Conclusion:** The lines intersect at $(-3, 5)$, so the system has exactly one solution. **Final answer:** The system has one solution at $(-3, 5)$.