Determine whether the system is inconsistent, dependent, or neither.
-$$\left\{ \begin{array} { l }
x - y + 2 z = - 5 \
3 x + z = 0 \
- x + y - 2 z = 20
\end{array} \right.$$
A) neither
B) dependent
C) inconsistent

Question

Determine whether the system is inconsistent, dependent, or neither.
-$$\left\{ \begin{array} { l } 
x - y + 2 z = - 5 \
3 x + z = 0 \
- x + y - 2 z = 20
\end{array} \right.$$
A) neither
B) dependent
C) inconsistent

Quizplus · Accepted Answer

The system is inconsistent because the third equation is a multiple of the first equation with a different constant term, leading to a contradiction.

Determine Whether the System Is Inconsistent, Dependent, or Neither {x−y+2z=−53x+z=0−x+y−2z=20\left\{ \begin{array} { l } x - y + 2 z = - 5 \\3 x + z = 0 \\- x + y - 2 z = 20\end{array} \right.⎩⎨⎧​x−y+2z=−53x+z=0−x+y−2z=20​

Determine Whether the System Is Inconsistent, Dependent, or Neither $\left\{ \begin{array} { l } x - y + 2 z = - 5 \\3 x + z = 0 \\- x + y - 2 z = 20\end{array} \right.$