How to find $x$ , $y$ and $z$ from this matrix?
$\begin{array}{ccc|c} 1 & 1 & 1 & 1\\ 1 & -1 & -1 & 0\\ 2 & 2 & 0 & -1\\ 1 & 0 & 1 & 5 \\ 1 & -1 & 4 & 3 \\ \end{array}$
As usual i began with Gaussian elimination and i've got matrix with three different $z$ values.
$\begin{array}{ccc|c} 1 & 1 & 1 & 1\\ 0 & -1 & 0 & 4\\ 0 & 0 & 3 & -6\\ 0 & 0 & -2 & -9 \\ 0 & 0 & -2 & -3 \\ \end{array}$
My question is, is it possible to find solution for this matrix because if we eliminate $-2$ from last row we get contradiction $0=15$. Should that mean that matrix has no solution or maybe we could just remove that row because for solving the matrix $rang =4$ is enough? How should i proceed and find solution?
The last $2$ rows say
$-2z=-9$ and $-2z=-3$.
Thus, no solution exists.