The prior estimate and decaypropertyof positive solutions are derived for a system of quasilinear elliptic diserential equations 3rst. Then, the nonexistence result for radiallynonincreasing positive solutions of the sys11 tem is implied. Byusing this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian 3ltration systems) are established to extend the result for semilinear reaction-disusion 13 systems (Fujita type).