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Q-conditional symmetries (nonclassical symmetries) for a general class oftwo-component reaction-diffusion systems with constant diffusivities arestudied. Using the recently introduced notion of Q-conditional symmetries ofthe first type (R. Cherniha J. Phys. A: Math. Theor., 2010. vol. 43., 405207),an exhaustive list of reaction-diffusion systems admitting such symmetry isderived. The form-preserving transformations for this class of systems areconstructed and it is shown that this list contains only non-equivalentsystems. The obtained symmetries permit to reduce the reaction-diffusionsystems under study to two-dimensional systems of ordinary differentialequations and to find exact solutions. As a non-trivial example, multiparameterfamilies of exact solutions are explicitly constructed for two nonlinearreaction-diffusion systems. A possible interpretation to a biologicallymotivated model is presented.

Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations