  Large systems of linear equations are ubiquitous in science. Quite often,
e.g. when considering population dynamics or chemical networks, the solutions
must be non-negative. Recently, it has been shown that large systems of random
linear equations exhibit a sharp transition from a phase, where a non-negative
solution exists with probability one, to one where typically no such solution
may be found. The critical line separating the two phases was determined by
combining Farkas' lemma with the replica method. Here, we show that the same
methods remain viable to characterize the two phases away from criticality. To
this end we analytically determine the residual norm of the system in the
unsolvable phase and a suitable measure of robustness of solutions in the
solvable one. Our results are in very good agreement with numerical
simulations.
