Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$\begin{aligned}
& x-y+2 z=11 \
& -2 x+2 y-4 z=3 \
& x+4 y+z=23
\end{aligned}$

A) $\{(x, y, z) \mid x-y+2 z=11\}$; dependent equations
B) $\{(0,5,3)\}$
C) $\{(3,0,5)\}$
D) $\varnothing$; inconsistent system

Question

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$\begin{aligned}
& x-y+2 z=11 \
& -2 x+2 y-4 z=3 \
& x+4 y+z=23
\end{aligned}$

A) $\{(x, y, z) \mid x-y+2 z=11\}$; dependent equations
B) $\{(0,5,3)\}$
C) $\{(3,0,5)\}$
D) $\varnothing$; inconsistent system

Quizplus · Accepted Answer

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

Solve the System of Equations x−y+2z=11−2x+2y−4z=3x+4y+z=23\begin{aligned}& x-y+2 z=11 \\& -2 x+2 y-4 z=3 \\& x+4 y+z=23\end{aligned}​x−y+2z=11−2x+2y−4z=3x+4y+z=23​

Solve the System of Equations $\begin{aligned}& x-y+2 z=11 \\& -2 x+2 y-4 z=3 \\& x+4 y+z=23\end{aligned}$