1. **State the problem:** Solve the equation $x + y = 2$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $x$ from both sides of the equation. This uses the rule that you can perform the same operation on both sides of an equation without changing its equality. 3. **Intermediate work:** $$x + y = 2$$ Subtract $x$ from both sides: $$\cancel{x} + y = 2 - \cancel{x}$$ 4. **Simplify:** $$y = 2 - x$$ 5. **Explanation:** We have expressed $y$ as a function of $x$. For any value of $x$, you can find $y$ by subtracting $x$ from 2. **Final answer:** $$y = 2 - x$$