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.
-$$\begin{array} { l }
x - 8 y + z = 6 \
3 x - y + 2 z = 7
\end{array}$$
A) $\left\{ \left( \frac { 50 } { 23 } , - \frac { 11 } { 23 } , 1 \right) \right\}$
B) $\varnothing$
C) $\left\{ \left( \frac { - 50 - 15 z } { 25 } , \frac { 11 + z } { 25 } , z \right) \right\}$
D) $\left\{ \left( \frac { 50 - 15 z } { 23 } , \frac { - 11 + z } { 23 } , z \right) \right\}$

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.
-$$\begin{array} { l } 
x - 8 y + z = 6 \
3 x - y + 2 z = 7
\end{array}$$
A) $\left\{ \left( \frac { 50 } { 23 } , - \frac { 11 } { 23 } , 1 \right) \right\}$
B) $\varnothing$
C) $\left\{ \left( \frac { - 50 - 15 z } { 25 } , \frac { 11 + z } { 25 } , z \right) \right\}$
D) $\left\{ \left( \frac { 50 - 15 z } { 23 } , \frac { - 11 + z } { 23 } , z \right) \right\}$

Quizplus · Accepted Answer

The system of equations has two equations and three unknowns, which typically leads to infinitely many solutions. By applying the Gauss-Jordan method, we can reduce the system to a form where one of the variables can be chosen arbitrarily (in this case, $z$). The correct solution set expresses $x$ and $y$ in terms of $z$, indicating that there are infinitely many solutions depending on the value of $z$.

Use the Gauss-Jordan Method to Solve the System of Equations x−8y+z=63x−y+2z=7\begin{array} { l } x - 8 y + z = 6 \\3 x - y + 2 z = 7\end{array}x−8y+z=63x−y+2z=7​

Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array} { l } x - 8 y + z = 6 \\3 x - y + 2 z = 7\end{array}$