1. **State the problem:** Solve the system of equations: $$x + 2y = 5$$ $$y = 3 - x$$ 2. **Use substitution method:** Since the second equation gives $y$ in terms of $x$, substitute $y = 3 - x$ into the first equation. 3. **Substitute and simplify:** $$x + 2(3 - x) = 5$$ $$x + 6 - 2x = 5$$ 4. **Combine like terms:** $$\cancel{x} + 6 - \cancel{2x} = 5$$ $$-x + 6 = 5$$ 5. **Isolate $x$:** $$-x = 5 - 6$$ $$-x = -1$$ 6. **Solve for $x$:** $$x = 1$$ 7. **Find $y$ by substituting $x=1$ into $y = 3 - x$:** $$y = 3 - 1 = 2$$ **Final answer:** $$x = 1, \quad y = 2$$