\(\begin{eqnarray*} 2 x - 5 y + 2 z &=&~~~0\\ x + 3 y + ~~z &=& -1\\ y - 3 z &=&~~~0 \end{eqnarray*}\qquad\qquad \left[\begin{array}{rrr|r} 2 & -5 & 2 & 0\\ 1 & 3 & 1 & -1\\ 0 & 1 & -3 & 0 \end{array}\right]\)
\(D=\left|\begin{array}{rrr} 2 & -5 & 2\\ 1 & 3 & 1\\ 0 & 1 & -3 \end{array}\right|=-33\)
\(D_x=\left|\begin{array}{rrr} 0 & -5 & 2\\ -1 & 3 & 1\\ 0 & 1 & -3 \end{array}\right|=13,\qquad D_y=\left|\begin{array}{rrr} 2 & 0 & 2\\ 1 & -1 & 1\\ 0 & 0 & -3 \end{array}\right|=6,\qquad D_z=\left|\begin{array}{rrr} 2 & -5 & 0\\ 1 & 3 & -1\\ 0 & 1 & 0 \end{array}\right|=2\)
\(x=\dfrac{D_x}{D}=-\dfrac{13}{33}\)
\(y=\dfrac{D_y}{D}=-\dfrac{6}{33}\)
\(z=\dfrac{D_z}{D}=-\dfrac{2}{33}\)
So the solution is \(\left(-\dfrac{13}{33}, -\dfrac{6}{33}, -\dfrac{2}{33}\right).\)