Question

The system of equations; $2x+6y+11=0,6y-18z+1=0$ and $6x+20y-6z+3=0$

• A. is consistent
• B. has a unique solution
• C. is inconsistent
• D. cannot be determined

Answer 1

Answer: (C)

is inconsistent

The given system of equations can be written as $AX=B$
where $A=\left[\begin{array}{ccc}2& 6& 0\\ 0& 6& -18\\ 6& 20& -6\end{array}\right]$, $X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right],B=\left[\begin{array}{c}-11\\ -1\\ -3\end{array}\right]$
Here, $D=|A|=\left|\begin{array}{ccc}2& 6& 0\\ 0& 6& -18\\ 6& 20& -6\end{array}\right|$
$D=0$
Now, $D_1=\left|\begin{array}{ccc}-11& 6& 0\\ -1& 6& -18\\ -3& 20& -6\end{array}\right|$
$\Rightarrow D_1=-3276\ne 0$
As, $D=0$ and at least one of $D_1,D_2,D_3$ is non-zero, the system of equation is inconsistent and has no solution.
Hence, option 'C' is correct.