1. **Problem:** Given the equation $\frac{x - 2y}{2 + 3y} = \frac{1}{3}$, find $\frac{y}{x}$. Also given are the equations $x - 2y = 3$ and $x + 3y = 1$. 2. **Step 1:** Use the given equations to find $x$ and $y$. From $x - 2y = 3$, we have: $$x = 3 + 2y$$ Substitute into $x + 3y = 1$: $$3 + 2y + 3y = 1$$ $$5y = 1 - 3$$ $$5y = -2$$ $$y = -\frac{2}{5}$$ 3. **Step 2:** Find $x$ using $y$: $$x = 3 + 2\left(-\frac{2}{5}\right) = 3 - \frac{4}{5} = \frac{15}{5} - \frac{4}{5} = \frac{11}{5}$$ 4. **Step 3:** Calculate $\frac{y}{x}$: $$\frac{y}{x} = \frac{-\frac{2}{5}}{\frac{11}{5}} = -\frac{2}{5} \times \frac{5}{11} = -\frac{2}{11}$$ **Final answer:** $$\boxed{\frac{y}{x} = -\frac{2}{11}}$$