1. **Problem statement:** Solve the system of equations using the substitution method for part (a): I: $3x - 4y = 18$ II: $2y - 5x = 12$ 2. **Substitution method formula:** We solve one equation for one variable and substitute into the other. 3. **Step 1:** Solve equation I for $x$: $$3x - 4y = 18 \implies 3x = 18 + 4y \implies x = \frac{18 + 4y}{3}$$ 4. **Step 2:** Substitute $x = \frac{18 + 4y}{3}$ into equation II: $$2y - 5\left(\frac{18 + 4y}{3}\right) = 12$$ 5. **Step 3:** Multiply both sides by 3 to clear denominator: $$3 \times 2y - 3 \times 5 \left(\frac{18 + 4y}{3}\right) = 3 \times 12$$ $$6y - 5(18 + 4y) = 36$$ 6. **Step 4:** Distribute and simplify: $$6y - 90 - 20y = 36$$ $$6y - 20y = 36 + 90$$ $$-14y = 126$$ 7. **Step 5:** Solve for $y$: $$y = \frac{126}{-14} = -9$$ 8. **Step 6:** Substitute $y = -9$ back into $x = \frac{18 + 4y}{3}$: $$x = \frac{18 + 4(-9)}{3} = \frac{18 - 36}{3} = \frac{-18}{3} = -6$$ 9. **Final answer:** $$\boxed{x = -6, y = -9}$$ This completes the solution for the first system using substitution.