Solve the system.
-$$\left\{ \begin{array} { c }
x - y + 4 z = - 2 \
4 x + z = 0 \
- x + y - 4 z = 4
\end{array} \right.$$
A) $( 0,2,0 )$
B) $( 0,0,2 )$
C) $\varnothing$
D) $( 4,2,0 )$

Question

Solve the system.
-$$\left\{ \begin{array} { c } 
x - y + 4 z = - 2 \
4 x + z = 0 \
- x + y - 4 z = 4
\end{array} \right.$$
A) $( 0,2,0 )$
B) $( 0,0,2 )$
C) $\varnothing$
D) $( 4,2,0 )$

Quizplus · Accepted Answer

Adding the first and third equations cancels out $y$ and $z$, resulting in $0 = 2$, which is a contradiction. This means there is no solution to the system, indicating it is inconsistent.

Solve the System {x−y+4z=−24x+z=0−x+y−4z=4\left\{ \begin{array} { c } x - y + 4 z = - 2 \\4 x + z = 0 \\- x + y - 4 z = 4\end{array} \right.⎩⎨⎧​x−y+4z=−24x+z=0−x+y−4z=4​

Solve the System $\left\{ \begin{array} { c } x - y + 4 z = - 2 \\4 x + z = 0 \\- x + y - 4 z = 4\end{array} \right.$