Apart from the typos, which Alan pointed out, it is noticeable, that your system has an infinite number of solutions. The rank of the 7x7 coefficient matrix it only 2. Depending on the rank of the extended matrix in your case you can chose 5 variables as you like and calculate the remaining 2.
If you solve numerically, Mathcad choses the "inner" five variables to be zero and calculates A and G. If you evaluate symbolically, the symbol processor choses the last five variables to be zero and calculates A and B.
If you use "fully" with the symbolic eval, Mathcad shows you how to calculate A and B if you chose the remaining five to be any values you wish.
I have no idea where these equations stem from, but I could image, that it should be a(B,C,D,E,F,G)=A (instead of =0) and so on with the rest. You will get a nice unique solution that way - just a guess.