Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l }
3 x + y - 4 z = 0 \
- x - 2 y + 2 z = 4 \
5 x + 5 y - 8 z = - 8
\end{array}$$
A)inconsistent
B)dependent
C)neither

Question

Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l } 
3 x + y - 4 z = 0 \
- x - 2 y + 2 z = 4 \
5 x + 5 y - 8 z = - 8
\end{array}$$
A)inconsistent
B)dependent
C)neither

Quizplus · Accepted Answer

The system is dependent because the third equation is a multiple of the first equation (multiplied by 5/3), indicating that there are infinitely many solutions. This means the equations are not independent, and the system does not have a unique solution.

Determine Whether the System Is Inconsistent, Dependent, or Neither 3x+y−4z=0−x−2y+2z=45x+5y−8z=−8\begin{array} { l } 3 x + y - 4 z = 0 \\- x - 2 y + 2 z = 4 \\5 x + 5 y - 8 z = - 8\end{array}3x+y−4z=0−x−2y+2z=45x+5y−8z=−8​

Determine Whether the System Is Inconsistent, Dependent, or Neither $\begin{array} { l } 3 x + y - 4 z = 0 \\- x - 2 y + 2 z = 4 \\5 x + 5 y - 8 z = - 8\end{array}$