Use Gauss-Jordan Elimination to Solve the Linear System and Determine $$\begin{array} { l } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array}$$

question 39

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.
- $$\begin{array} { l } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array}$$

• A) \(\left( \frac { 27 } { 5 } , \frac { 13 } { 5 } , 1 \right)\)
• B) \(\left( - \frac { 7 } { 5 } z + \frac { 34 } { 5 } , \frac { 2 } { 5 } z + \frac { 11 } { 5 } , z \right)\)
• C) no solution
• D) \(\left( \frac { 3 } { 5 } z + \frac { 16 } { 5 } , - \frac { 8 } { 5 } z + \frac { 29 } { 5 } , z \right)\)

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