1. **State the problem:** We have two simultaneous equations: (1) $x - 4y = 12$ (2) $x - 2 = 6y$ We need to: a) Rearrange equation (2) to make $x$ the subject. b) Solve the simultaneous equations using substitution. 2. **Rearrange equation (2) to make $x$ the subject:** Starting with equation (2): $$x - 2 = 6y$$ Add 2 to both sides: $$x - 2 + 2 = 6y + 2$$ $$x = 6y + 2$$ 3. **Substitute $x = 6y + 2$ into equation (1):** Equation (1) is: $$x - 4y = 12$$ Substitute $x$: $$(6y + 2) - 4y = 12$$ 4. **Simplify and solve for $y$:** $$6y + 2 - 4y = 12$$ $$2y + 2 = 12$$ Subtract 2 from both sides: $$2y + 2 - 2 = 12 - 2$$ $$2y = 10$$ Divide both sides by 2: $$\frac{\cancel{2}y}{\cancel{2}} = \frac{10}{2}$$ $$y = 5$$ 5. **Find $x$ using $x = 6y + 2$:** Substitute $y = 5$: $$x = 6(5) + 2$$ $$x = 30 + 2$$ $$x = 32$$ 6. **Final answer:** $$x = 32, \quad y = 5$$