Solving linear system equation How would I solve this linear system equation?
$$\begin{cases} 
2w+x-y=4\\
3z-x=6\\
-2y-x+9z+4w=7 
\end{cases}$$
First I arranged them so I could make the metric and then I was stuck and I don't realy know how to continue, please help me.

$$2w+x-y=4$$
$$3z-x=6$$
$$-2y-x+9z+4w=7$$
Can be rewritten to
$$2w+x-y+0z=4$$
$$0w-x+0y+3z=6$$
$$4w-x-2y+9z=7$$
$$0w+0x+0y+0z=0$$
So now we have
$$\left[\begin{array}{cccc|c}
2 & 1 & -1 & 0 & 4 \\
0 & -1 & 0 & 3 & 6 \\
4 & -1 & -2 & 9 & 7 \\
0 & 0 & 0 & 0 & 0 \\
\end{array}\right]$$
$$=\left[\begin{array}{cccc|c}
2 & 1 & -1 & 0 & 4 \\
0 & -1 & 0 & 3 & 6 \\
0 & 3 & 0 & -9 & 1 \\
0 & 0 & 0 & 0 & 0 \\
\end{array}\right]$$
$$=\left[\begin{array}{cccc|c}
2 & 1 & -1 & 0 & 4 \\
0 & -1 & 0 & 3 & 6 \\
0 & 0 & 0 & 0 & 19 \\
0 & 0 & 0 & 0 & 0 \\
\end{array}\right]$$
This system is inconsistent because we have
$$0w+0x+0y+0z=19$$
Therefore this system has no solutions.
