Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array} { l } x - 8 y + z = 2 \\3 x - y + 2 z = 6\end{array}$

Multiple Choice

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable.
$\begin{array} { l } x - 8 y + z = 2 \\3 x - y + 2 z = 6\end{array}$

A) $\left\{ \left( \frac { - 46 - 15 z } { 25 } , \frac { 0 + z } { 25 } , z \right) \right\}$
B) $\{ ( 2,0,1 ) \}$
C) $\left\{ \left( \frac { 46 - 15 z } { 23 } , \frac { 0 + z } { 23 } , z \right) \right\}$
D) $\varnothing$