Let $a{oplus}b$ = max(a, b), $a{otimes}b$=a+b, a, $binmathbb{R}_{varepsilon};:=cup{-infty}$. In max-plus algebra we work on the linear algebra structure for the pair of operations (${oplus},{otimes}$) extended to matrices and vectors over $mathbb{R}_{varepsilon}$. In this paper our main aim is to reproduce the work of R. A. Cuninghame-Green [3] on the linear systems over a max-plus semi-field $mathbb{R}_{varepsilon}$.