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) $\varnothing$

Question

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) $\varnothing$

Quizplus · Accepted Answer

The system of equations has infinitely many solutions. By using the Gauss-Jordan method, we express the solution in terms of the arbitrary variable $ z $.

Use the Gauss-Jordan Method to Solve the System of Equations x−8y+z=23x−y+2z=6\begin{array} { l } x - 8 y + z = 2 \\3 x - y + 2 z = 6\end{array}x−8y+z=23x−y+2z=6​

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