1. **State the problem:** Solve the system of equations using row operations to reach echelon or reduced echelon form. The system given is: $$x + 2y = 0$$ 2. **Write the augmented matrix:** $$\begin{bmatrix} 1 & 2 & | & 0 \end{bmatrix}$$ 3. **Apply row operations:** Since this is a single equation with two variables, the matrix is already in echelon form. 4. **Interpret the solution:** The equation $x + 2y = 0$ can be rewritten as: $$x = -2y$$ This means $x$ depends on $y$, and there are infinitely many solutions along the line defined by this equation. 5. **Express the solution set:** $$\{(x,y) \mid x = -2t, y = t, t \in \mathbb{R}\}$$ This is the parametric form where $t$ is any real number. **Final answer:** The solution is all points $(x,y)$ such that $x = -2y$ or equivalently $x = -2t$, $y = t$ for any real $t$.