The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimate for a class quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reactiondiffusion (Fujita type) systems.