Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r r }
x - y + 2 z = & - 2 \
4 x + z = & 0 \
- x + y - 2 z = & 6
\end{array} \right.$$
A) infinitely many solutions; dependent equations
B) $\{ ( 0,0,2 ) \}$
C) $\{ ( 2,2,0 ) \}$
D) no solution or $\varnothing$

Question

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r r } 
x - y + 2 z = & - 2 \
4 x + z = & 0 \
- x + y - 2 z = & 6
\end{array} \right.$$
A) infinitely many solutions; dependent equations
B) $\{ ( 0,0,2 ) \}$
C) $\{ ( 2,2,0 ) \}$
D) no solution or $\varnothing$

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.

Solve the System {x−y+2z=−24x+z=0−x+y−2z=6\left\{ \begin{array} { r r } x - y + 2 z = & - 2 \\4 x + z = & 0 \\- x + y - 2 z = & 6\end{array} \right.⎩⎨⎧​x−y+2z=4x+z=−x+y−2z=​−206​

Solve the System $\left\{ \begin{array} { r r } x - y + 2 z = & - 2 \\4 x + z = & 0 \\- x + y - 2 z = & 6\end{array} \right.$