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A simple system of coupled kinetic equations for quark and gluon anisotropic systems is solved numerically. The solutions are compared with the predictions of the anisotropic hydrodynamics describing a mixture of anisotropic fluids. We find that the solutions of the kinetic equations can be well reproduced by anisotropic hydrodynamics if the initial distribution are oblate for both quarks and gluons. On the other hand, the solutions of the kinetic equations have a different qualitative behavior from those obtained in anisotropic hydrodynamics if the initial configurations are oblate-prolate or prolate-prolate. This suggests that an extension of the anisotropic hydrodynamics scheme for the mixture of anisotropic fluids is needed, where higher moments of the kinetic equations are used and present simplifications are avoided.