Solve the linear system with the given augmented matrix (the last column should have the dots before it but I'm not sure how to enter those)

$\displaystyle

\begin{pmatrix}4 & 2 & -1 & 5\\3 & 3 & 6 & 1\\5 & 1 & -8 & 8\end{pmatrix}

$

First I subtracted the 2nd row from the 1st to get:

$\displaystyle

\begin{pmatrix}1 & -1 & -7 & 4\\3 & 3 & 6 & 1\\5 & 1 & -8 & 8\end{pmatrix}

$

Then I subtracted 3 x row 1 from row 2 and 5 x row 1 from row 3 to get:

$\displaystyle

\begin{pmatrix}1 & -1 & -7 & 4\\0 & 6 & 27 & -11\\0 & 6 & 27 & -12\end{pmatrix}

$

I subtracted row 3 from row 2 to get:

$\displaystyle

\begin{pmatrix}1 & -1 & -7 & 4\\0 & 0 & 0 & 1\\0 & 6 & 27 & -12\end{pmatrix}

$

Since I have a row of 0 0 0 1, I believe there is no solution. Am I doing this wrong? or maybe missed a step?