Why can't I find any solution of this three equations? $$2x+6y-z=10$$
$$3x+2y+2z=1$$
$$5x+4y+3z=4$$
I do not find any solution of this three equations.I know that if two equations or planes are parallel then we do't find any solution.But I can't understand what is the problem here.Are they parallel.and if they are parallel How can I understand that.please  help me.

Note that 
$$\ det\begin{pmatrix}
2 & 6 & -1 \\ 
3 & 2  &  2 \\ 
5 & 4  &  3
\end{pmatrix}= 0$$ while $$rank \begin{pmatrix}
2 & 6 & -1 & 10\\ 
3 & 2  &  2 &   1\\ 
5 & 4  &  3 &   4
\end{pmatrix}=3$$
because $$\begin{vmatrix}
6 & -1  & 10 \\ 
2 &  2 &     1\\ 
4 &  3 &    4
\end{vmatrix} \neq 0$$ so the system has no solutions.
On the other hand reducing the augmented matrix
$$
\begin{pmatrix}
2 & 6 & -1 & 10\\ 
3 & 2  &  2 &   1\\ 
5 & 4  &  3 &   4 
\end{pmatrix}
$$
$$
\longrightarrow 
\begin{pmatrix}
2 & 6 & -1 & 10\\ 
0 & -2  &  1 &   -7\\ 
0 & 0  &  0 &   35
\end{pmatrix}
$$. Seeing the last row you realize that can't be possible.
