I have a system of linear equations that has no solutions.
It looks like this in augmented matrix form.
\begin{array}{ccc|c}1&-1&2&5\\2&1&0&1\\1&8&-1&3\\-1&-5&-12&41\end{array}
I need to replace right hand value in equation 4 (41) with a value that will give me a unique solution when in reduced row echelon form. How do I approach this problem in a logical way to find the possible values?