1. **State the problem:** Solve the system of equations using the substitution method: $$2m + n = 0$$ $$m + 2n = 3$$ 2. **Isolate one variable:** From the first equation, solve for $n$ in terms of $m$: $$2m + n = 0 \implies n = -2m$$ 3. **Substitute into the second equation:** Replace $n$ with $-2m$ in the second equation: $$m + 2(-2m) = 3$$ 4. **Simplify and solve for $m$:** $$m - 4m = 3$$ $$\cancel{m} - 4\cancel{m} = 3$$ $$-3m = 3$$ Divide both sides by $-3$: $$\frac{-3m}{\cancel{-3}} = \frac{3}{\cancel{-3}} \implies m = -1$$ 5. **Find $n$ using $m = -1$:** Substitute back into $n = -2m$: $$n = -2(-1) = 2$$ 6. **Final answer:** $$m = -1, \quad n = 2$$