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.
-$$\begin{array} { c }
- 4 x - 7 y - z = - 67 \
x + 6 y - 2 z = 20 \
9 x + y + z = 67
\end{array}$$
A) $\varnothing$
B) $\{ ( 6,5,8 ) \}$
C) $\{ ( - 6,5,12 ) \}$
D) $\{ ( 6,8,5 ) \}$

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.
-$$\begin{array} { c } 
- 4 x - 7 y - z = - 67 \
x + 6 y - 2 z = 20 \
9 x + y + z = 67
\end{array}$$
A) $\varnothing$
B) $\{ ( 6,5,8 ) \}$
C) $\{ ( - 6,5,12 ) \}$
D) $\{ ( 6,8,5 ) \}$

Quizplus · Accepted Answer

The system of equations given can be solved using the Gauss-Jordan method, which involves row reducing the augmented matrix of the system to its reduced row echelon form. After performing the necessary row operations to achieve this form, the solution to the system can be directly read off as $x = 6$, $y = 5$, and $z = 8$, which corresponds to the single solution set $\{ ( 6,5,8 ) \}$. This indicates that the system has a unique solution.

Use the Gauss-Jordan Method to Solve the System of Equations −4x−7y−z=−67x+6y−2z=209x+y+z=67\begin{array} { c } - 4 x - 7 y - z = - 67 \\x + 6 y - 2 z = 20 \\9 x + y + z = 67\end{array}−4x−7y−z=−67x+6y−2z=209x+y+z=67​

Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array} { c } - 4 x - 7 y - z = - 67 \\x + 6 y - 2 z = 20 \\9 x + y + z = 67\end{array}$