1. **State the problem:** Solve the system of equations: $$y = -x + 3$$ $$y = 2x$$ 2. **Choose a method:** Since both equations are equal to $y$, we can use the substitution method by setting the right sides equal to each other. 3. **Set the equations equal:** $$-x + 3 = 2x$$ 4. **Solve for $x$:** Add $x$ to both sides: $$-x + 3 + x = 2x + x$$ $$3 = 3x$$ Divide both sides by 3: $$\frac{3}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$1 = x$$ 5. **Find $y$ by substituting $x=1$ into one of the original equations:** Using $y = 2x$: $$y = 2(1) = 2$$ 6. **Solution:** The solution to the system is $\boxed{(1, 2)}$. 7. **Explanation:** We used substitution because both equations were already solved for $y$, making it easy to set them equal and solve for $x$. Then we substituted back to find $y$.