Answer:
System has equal number of unknowns and equations.
Manipulation easily yielded expressions for 4 of the 7 unknowns.
However it seems that the remaining 3 unknowns x,y,z are not fixed by the equations. Different combinations (x0,y0,z0) seem possible without violating the system equations.
Is this possible, or did I most probably make a mistake in counting degrees of freedom?
Explanation: