In this article, we consider the system of differential equations ÀD pðxÞ u ¼ k pðxÞ ½aðxÞu aðxÞ v cðxÞ þ h 1 ðxÞ in X; where X & R N is a bounded domain with C 2 -boundary @X; 1 < pðxÞ; qðxÞ 2 C 1 ðXÞ are functions. The operator ÀD p(x) u = À div(OEÑuOE p(x)À2 Ñu) is called the p(x)-Laplacian. When a, b, d, c satisfy some suitable conditions, we prove the existence of positive solution via sub-supersolution arguments without assuming sign conditions on the functions h 1 and h 2 .