The paper is devoted to the Barenblatt model of oil and water filtration with an admixture of active reagents. This model is used in oil production for hard-to-recover deposits by chemical flooding. The model is described by a system of two first order nonlinear partial differential equations. Conditions for the Buckley–Leverett function, under which the system is reduced to a linear one using symplectic transformations, are found. This makes possible to find classes of exact general solutions of the Barenblatt system and to solve the Cauchy problem.