First of all many thanks to you two to make me aware of such great methods.
I have tried with DirectSearch package, and unfortunately it is not giving me satisfactory results (the constraint is all x1, x2 .. x7 should be between 0.1 and 0.9, and x8 between 0.1 and 0.5. The solutions on back-substitution are not satisying the equations, leaving a significant remainder).
Now, I want to try Draghilev Method, I have looked into the examples provided on this forum, but could not get success. I have two objectives: First, I want to solve this system (restricting all x1, x2......x7 between 0.1 and 0.9, and x8 between 0.1 and 0.5), and second I want to plot variable x8 against 'a'. How can I do this efficiently. The worksheet is here Alg_equation_trans.mw.
Many thanks in advance.