1. **State the problem:** Solve the linear equation $5 - 2y = 7$ for $y$. 2. **Use the formula and rules:** To solve for $y$, isolate $y$ on one side by performing inverse operations. 3. **Step-by-step solution:** Start with the equation: $$5 - 2y = 7$$ Subtract 5 from both sides: $$5 - 2y - 5 = 7 - 5$$ $$\cancel{5} - 2y - \cancel{5} = 2$$ $$-2y = 2$$ Divide both sides by $-2$: $$\frac{-2y}{-2} = \frac{2}{-2}$$ $$y = -1$$ 4. **Answer:** The solution is $y = -1$.