1. **State the problem:** Solve the equation $\beta y = y + \frac{8}{13}$ for $y$. 2. **Rewrite the equation:** $$\beta y = y + \frac{8}{13}$$ 3. **Isolate terms involving $y$ on one side:** $$\beta y - y = \frac{8}{13}$$ 4. **Factor out $y$:** $$y(\beta - 1) = \frac{8}{13}$$ 5. **Divide both sides by $(\beta - 1)$ to solve for $y$:** $$y = \frac{\frac{8}{13}}{\beta - 1} = \frac{8}{13(\beta - 1)}$$ 6. **Important note:** This solution is valid only if $\beta \neq 1$ because division by zero is undefined. **Final answer:** $$y = \frac{8}{13(\beta - 1)}$$