Solving the problem of embedding a two-metricphenomenologically symmetric geometry of rank $ (3,2) $ with the function $ g(x,y,\xi,\eta)=(g^{1},g^{2})=(x\xi+y\ mu,x\eta+y\nu) $ into an affine two-metric phenomenologically symmetric geometry of rank $ (4,2) $ withthe function $ f(x,y,\xi,\eta,\mu,\nu)=(f^{1},f^{2})=(x\xi+y\mu+\rho,x\eta+y\nu+\tau) $ leads to the problemof establishing the existence of nondegenerate solutions to the corresponding system $ f(\bar{x},\bar{y},\bar{\xi},\bar{\eta},\bar{\mu},\bar{\nu})=\chi(g(x,y,\xi,\eta),\mu,\nu) $ of two functionalequations. This systemwritten explicitly as $ \bar{x}\bar{\xi}+\bar{y}\bar{\mu}+\bar{\rho}=\chi^{1}(x\xi+y\mu,x\eta+y\nu,\mu,\nu) $ , $ \bar{x}\bar{\eta}+\bar{y}\bar{\nu}+\bar{\tau}=\chi^{2}(x\xi+y\mu,x\eta+y\nu,\mu,\nu) $ is solved provided that $ g $ and $ f $ were known.To find a general nondegeneratesolution to the system, we differentiate with respect to the variables $ x $ , $ y $ and $ \xi $ , $ \eta $ , $ \mu $ , $ \nu $ to obtain a system of differential equations with some matrix ofcoefficients $ A $ .Reducing $ A $ to Jordan form, we solve the corresponding system of differential equationsarriving at a nondegenerate solution to the original system.
