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A general solution for a coupled system of eikonal equations u_\mu u_\mu = 0,v_\mu v_\mu = 0, u_\mu v_\mu = 1 is presented, where lower indices designatederivatives, \mu = 0, 1, 2 and summation is implied over the repeated indices.This solution is of interest by itself due to wide applications of the eikonalequations, but the system considered also appears to be part of the reductionconditions for many equations of mathematical physics. We describe in detailthe procedure that allowed obtaining of the general solution using hodographand contact transformations of the initial system, however, we omit herespecial case when the system is equivalent to a system for one space dimensionor to a system for one dependent function. The procedure used allowed alsoobtaining of the general solution for a coupled system of the eikonal andHamilton-Jacobi equation.

General Solution for a Coupled System of Eikonal Equations in Two Space Variables