Consider the following non-homogeneous system of equations where $x,y,z$ are variables and for a constant $\mathrm C$, $y \times z = \mathrm C \neq 0$
\begin{equation} \left\{ \begin{array}{lcl} a_1x + b_1y + c_1z &= d_1\\ a_2x + b_2y + c_2z &= d_2\\ \end{array} \right. \end{equation}
The most straightforward solution is to replace $z$ by $\dfrac{\mathrm C}{y}$ and convert this to a system of two nonlinear equations with two variables. I would like to know
- Is there another solution to this system?
- Is there any necessary and sufficient conditions for solvability of this system?
The homogeneous model of this problem already asked in Solving a system of two equations and three variables where product of two of the variables are constant and very good answers are given.
Thanks in advance