1. **State the problem:** Solve the linear equation $13y + 4 = 5y - 3$ for $y$. 2. **Write down the equation:** $$13y + 4 = 5y - 3$$ 3. **Isolate the variable terms on one side:** Subtract $5y$ from both sides: $$13y + 4 - 5y = 5y - 3 - 5y$$ $$\cancel{13y} + 4 + \cancel{-5y} = \cancel{5y} - 3 - \cancel{5y}$$ $$8y + 4 = -3$$ 4. **Isolate the constant term:** Subtract 4 from both sides: $$8y + 4 - 4 = -3 - 4$$ $$8y + \cancel{4} - \cancel{4} = -7$$ $$8y = -7$$ 5. **Solve for $y$ by dividing both sides by 8:** $$\frac{8y}{8} = \frac{-7}{8}$$ $$\cancel{8}y / \cancel{8} = -\frac{7}{8}$$ $$y = -\frac{7}{8}$$ **Final answer:** $$y = -\frac{7}{8}$$