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

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Final Answer: The solution to the system of equations is $x = - 4, y = - 5, z = 2$ .

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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 $x = - 4, y = - 5, z = 2$ .

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with z arbitrary.x+y−3z=−153x−3y+2z=7x+3y−3z=−25

Answer

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