Use Gauss-Jordan Elimination to solve the system by first converting it to an augmented matrix and then performing systematic row reduction. If the system has an infinite number of solutions, express them in terms of the parameter z. \[ \left\{\begin{array}{l} x+2z=0 \\ 3x-y+9z=0 \\ 3x+6z=0 \end{array}\right. \]
