System of three non linear equations with three unknowns with random coefficients

Question

I have the system of equations: $$ \begin{cases} Ax + By + Cz &= D \\ Exy + Fxz + Gyz &= H \\ Ixyz &= J \\ \end{cases} $$ Where $A,B,C,D,E,F,G,H,I,J$ are constant integers between 1 and 9.

$x,y,z$ are the three variables that have to be functions of the letters above, and the system has to meet equality in all cases. I tried substitution of variables but I cannot do it with the nonlinear equations

Any contribution is highly appreciated :)

Answer 1

Below equation has numerical solution:

$\begin{cases} Ax + By + Cz &= D \\ Exy + Fxz + Gyz &= H \\ Ixyz &= J \\ \end{cases}$

$(x,y,z)=(2,1,1)$

$(A,B,C)=(2,3,1)$

$(E,F,G)=(1,2,3)$

$(D,H,I,J)=(8,9,1,2)$