Use Matrices to Solve the System of Equations (If Possible) $$\left\{ \begin{array} { l } 7 x - 3 y - 9 z = 22 \\2 x + y + 3 z = - 3 \\2 x - 7 y - 3 z = - 17\end{array} \right.$$

Multiple Choice

Use matrices to solve the system of equations (if possible) . Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
$$\left\{ \begin{array} { l } 7 x - 3 y - 9 z = 22 \\2 x + y + 3 z = - 3 \\2 x - 7 y - 3 z = - 17\end{array} \right.$$

A) $x = - 1 , y = - 4 , z = - 3$
B) $x = 1 , y = - 4 , z = - 3$
C) $x = 1 , y = 4 , z = - 3$
D) $x = 4 , y = - 1 , z = 3$
E) no solution