Summary: In this paper sufficient regularity and coercivity conditions for Minty and Stampacchia type variational inequality systems are offered. The typical results state that if the independent inequalities are solvable, and the functions involved are lower semicontinuous, then the system has also a solution, that is, a factorization principle holds. As an application, a variational inequality system consisting of two partial differential inequalities is considered. This result is analogous to that of Y.-Q. Chen
[J. Math. Anal. Appl. 231, No. 1, 177–192 (1999; Zbl 0934.47031
)] obtained for a variational inequality.