Puente Muñoz, María Jesús De LaLorenzo, Elisa2023-06-202023-06-202001-08-150024379510.1016/j.laa.2011.02.014https://hdl.handle.net/20.500.14352/57074An algorithm to give an explicit description of all the solutions to any tropical linear system A x=B x is presented. The given system is converted into a finite (rather small) number p of pairs (S,T) of classical linear systems: a system S of equations and a system T of inequalities. The notion, introduced here, that makes p small, is called compatibility. The particular feature of both S and T is that each item (equation or inequality) is bivariate, i.e., it involves exactly two variables; one variable with coefficient 1 and the other one with -1. S is solved by Gaussian elimination. We explain how to solve T by a method similar to Gaussian elimination. To achieve this, we introduce the notion of sub-special matrix. The procedure applied to T is, therefore, called sub-specialization.engjournal articlehttp://www.sciencedirect.com/science/journal/00243795open access512Tropical linear systemAlgorithmÁlgebra1201 Álgebra