1. **State the problem:** Solve the linear equation $2x + y = 1$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $2x$ from both sides of the equation. 3. **Intermediate work:** $$2x + y = 1$$ Subtract $2x$ from both sides: $$\cancel{2x} + y - \cancel{2x} = 1 - 2x$$ Simplifies to: $$y = 1 - 2x$$ 4. **Explanation:** We moved the term $2x$ to the right side by subtracting it from both sides, which isolates $y$ on the left side. This gives the equation of $y$ in terms of $x$. 5. **Final answer:** $$y = 1 - 2x$$