Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with $z$ arbitrary. \[ \begin{aligned} x+y-3 z & =-15 \\ 3 x-3 y+2 z & =7 \\ x+3 y-3 z & =-25 \end{aligned} \]

Step 1 ：We are given the system of equations: \[\begin{aligned} x+y-3 z & =-15 \\ 3 x-3 y+2 z & =7 \\ x+3 y-3 z & =-25 \end{aligned}\]

Step 2 ：We will use the Gauss-Jordan method to solve this system. This method involves performing row operations on an augmented matrix to bring it to reduced row echelon form.

Step 3 ：The reduced row echelon form of the matrix corresponds to the system of equations \(x = -4\), \(y = -5\), and \(z = 2\).

Step 4 ：Therefore, the solution to the system of equations is \(x = -4\), \(y = -5\), and \(z = 2\).

Step 5 ：Final Answer: The solution to the system of equations is \(\boxed{x = -4, y = -5, z = 2}\).