1. **State the problem:** Solve the system of equations using substitution method: $$x - 3y = 12.5$$ $$3y = -12x + 111$$ 2. **Rewrite the second equation to express $y$ in terms of $x$:** $$3y = -12x + 111$$ $$y = \frac{-12x + 111}{3}$$ 3. **Substitute $y$ into the first equation:** $$x - 3\left(\frac{-12x + 111}{3}\right) = 12.5$$ 4. **Simplify the substitution:** $$x - \cancel{3} \left(\frac{-12x + 111}{\cancel{3}}\right) = 12.5$$ $$x - (-12x + 111) = 12.5$$ 5. **Distribute the minus sign:** $$x + 12x - 111 = 12.5$$ 6. **Combine like terms:** $$13x - 111 = 12.5$$ 7. **Add 111 to both sides:** $$13x - 111 + 111 = 12.5 + 111$$ $$13x = 123.5$$ 8. **Divide both sides by 13:** $$\frac{13x}{\cancel{13}} = \frac{123.5}{\cancel{13}}$$ $$x = 9.5$$ 9. **Substitute $x = 9.5$ back into the expression for $y$:** $$y = \frac{-12(9.5) + 111}{3} = \frac{-114 + 111}{3} = \frac{-3}{3} = -1$$ **Final answer:** $$(x, y) = (9.5, -1)$$