Oh, yes, with numeric values the results are probably easy (as you said) to compute, but beside the numeric results, I want firstly to have the symbolic results.
Matlab, Maple, and even Mathcad can solve symbolically this system of equations.
Another question here will be: if we restrict the result to be a real one (and that is because Mathematica cannot solve symbolically this system of equations if we do not restrict the results to be real ones), and at some point we want to have/see even the complex results (of course, if they exist) of this system of equations, then what will we do? Or, maybe we can hope that system of equations like above one to have only the results that are real.
Also, do you know the answer for this question: if I want to set a condition for some variables in equations Eq1,...,Eq7, for example, to restrict L1 and L2 to be positive numbers (L1 >0, L2>0), how do I do that?