  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 designate
derivatives, \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 eikonal
equations, but the system considered also appears to be part of the reduction
conditions for many equations of mathematical physics. We describe in detail
the procedure that allowed obtaining of the general solution using hodograph
and contact transformations of the initial system, however, we omit here
special case when the system is equivalent to a system for one space dimension
or to a system for one dependent function. The procedure used allowed also
obtaining of the general solution for a coupled system of the eikonal and
Hamilton-Jacobi equation.
