1. **State the problem:** Solve the linear equation $2x + 5y = 7$ for one variable in terms of the other. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This involves subtracting $2x$ from both sides and then dividing by $5$. 3. **Isolate $y$:** $$2x + 5y = 7$$ Subtract $2x$ from both sides: $$\cancel{2x} + 5y - \cancel{2x} = 7 - 2x$$ which simplifies to $$5y = 7 - 2x$$ 4. **Divide both sides by 5:** $$y = \frac{7 - 2x}{5}$$ Show the division step with cancellation: $$y = \frac{\cancel{5} \cdot \frac{7 - 2x}{\cancel{5}}}{} = \frac{7 - 2x}{5}$$ 5. **Final answer:** $$y = \frac{7 - 2x}{5}$$ This expresses $y$ in terms of $x$ for the given linear equation.