Rephrasing of the problem posted earlier

My variables are seven, the control surface deflections which I need
to find. But they don't appear in these equations, rather aerodynamic
coefficients appear for which I have some experimental data to work
with. I have the value of these coefficients at some points ( the
control surface deflections which I have to find ultimately) , say
one of the control surface varied and other kept zeros. SO I can't
predict the value of these coefficients in unctional form neither
through interpolation because of the constraints.
Even if I can predict the value how do I solve these equaions now.
And these are not differential equations , rather algebraic
equations.

Thanks in Advance.
Sincere Regards
Vineet Singh
Junior undergrad
Aeor Engg
IIT Kanpur, India