Use Gauss-Jordan Elimination to Solve the Linear System and Determine $$\begin{array} { l } 5 x - y + z = 8 \\7 x + y + z = 6\end{array}$$

Multiple Choice

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
- $$\begin{array} { l } 5 x - y + z = 8 \\7 x + y + z = 6\end{array}$$

A) no solution
B) $( - z + 3,4 z + 7 , z )$
C) $\left( \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z , z \right)$
D) $\left( - \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z - \frac { 13 } { 6 } , z \right)$