Am I right in thinking that the following augmented matrix equation only has one solution:
$\begin{bmatrix} 0 & 1 & 0 & 4\\ 0 & 0 & 1 & 10 \end{bmatrix} $
i.e., if the unknown variables are x, y and z, it follows that $y = 4\ and \ z = 10 $ are the only known variables, hence there can only be one solution.