1. **State the problem:** Solve the system of equations: $$\frac{1}{2}x + 6y = 12$$ $$y = x + 15$$ 2. **Use substitution method:** Since the second equation gives $y$ in terms of $x$, substitute $y = x + 15$ into the first equation. 3. **Substitute and simplify:** $$\frac{1}{2}x + 6(x + 15) = 12$$ Expand the terms: $$\frac{1}{2}x + 6x + 90 = 12$$ 4. **Combine like terms:** $$\frac{1}{2}x + 6x = \frac{1}{2}x + \frac{12}{2}x = \frac{13}{2}x$$ So the equation becomes: $$\frac{13}{2}x + 90 = 12$$ 5. **Isolate $x$:** $$\frac{13}{2}x = 12 - 90$$ $$\frac{13}{2}x = -78$$ 6. **Solve for $x$ by dividing both sides:** $$x = \frac{-78}{\frac{13}{2}} = -78 \times \frac{2}{13}$$ Show cancellation: $$x = -\cancel{78} \times \frac{2}{\cancel{13}} = -6 \times 2 = -12$$ 7. **Find $y$ using $y = x + 15$:** $$y = -12 + 15 = 3$$ **Final answer:** $$x = -12, \quad y = 3$$