Question: Solve the equation $\frac{1}{3} y - 3 = \frac{1}{9} y$.
1. **State the problem:** We need to solve the equation $$\frac{1}{3} y - 3 = \frac{1}{9} y$$ for $y$.
2. **Write down the equation:** $$\frac{1}{3} y - 3 = \frac{1}{9} y$$
3. **Goal:** Get all terms with $y$ on one side and constants on the other.
4. **Subtract $\frac{1}{9} y$ from both sides:**
$$\frac{1}{3} y - \frac{1}{9} y - 3 = 0$$
5. **Find common denominator for the $y$ terms:**
$$\frac{3}{9} y - \frac{1}{9} y - 3 = 0$$
6. **Combine like terms:**
$$\frac{3 - 1}{9} y - 3 = 0$$
$$\frac{2}{9} y - 3 = 0$$
7. **Add 3 to both sides:**
$$\frac{2}{9} y = 3$$
8. **Multiply both sides by the reciprocal of $\frac{2}{9}$, which is $\frac{9}{2}$:**
$$y = 3 \times \frac{9}{2}$$
9. **Calculate the right side:**
$$y = \frac{27}{2}$$
**Final answer:** $$y = \frac{27}{2}$$