Solve the system. If there is no unique solution, label the system as either dependent or inconsistent. $$\begin{aligned}
2 x + y + 3 z & = 12 \
x - y + 4 z & = 5 \
- 4 x + 4 y - 4 z & = - 20
\end{aligned}$$
A) $( 4,1,2 )$
B) $( 1,4,2 )$
C) Dependent system (infinitely many solutions)
D) Inconsistent system (no solution)

Question

Solve the system. If there is no unique solution, label the system as either dependent or inconsistent. $$\begin{aligned}
2 x + y + 3 z & = 12 \
x - y + 4 z & = 5 \
- 4 x + 4 y - 4 z & = - 20
\end{aligned}$$ 
A) $( 4,1,2 )$
B) $( 1,4,2 )$
C) Dependent system (infinitely many solutions)
D) Inconsistent system (no solution)

Quizplus · Accepted Answer

The system is dependent because the third equation is -2 times the first equation, indicating the equations are not independent and thus have infinitely many solutions.

Solve the System 2x+y+3z=12x−y+4z=5−4x+4y−4z=−20\begin{aligned}2 x + y + 3 z & = 12 \\x - y + 4 z & = 5 \\- 4 x + 4 y - 4 z & = - 20\end{aligned}2x+y+3zx−y+4z−4x+4y−4z​=12=5=−20​

Solve the System $\begin{aligned}2 x + y + 3 z & = 12 \\x - y + 4 z & = 5 \\- 4 x + 4 y - 4 z & = - 20\end{aligned}$