The enumeration of the number of regions in hyperplane arrangements has been the subject of numerous works, in particular those by Pak, Postnikov and Stanley, Athanasiadis and Linusson, Hopkins and Perkinson on so-called graphical arrangements. These arrangements are defined by equations containing only 2 variables. I propose to present a technique for labelling the regions of several classical arrangements (extended Shi arrangement, Fuss-Catalan) using two results. On the one hand, a variant of Farkas' Lemma giving existence conditions for solutions in linear inequalities and, on the other hand, the cycle decomposition of flows in a graph.