You're first evaluation is incorrect... If you solve the first equation for you get:
Plug this into the second equation to get:
That's why the other answers don't work, because they are not solutions to the system.
Lets take a simple system of two equations:
after evaluating a_{1} from the first equation and putting it into the second we get
this gives
so, solutions are: q=1, q=-1 and q=
but if you try to put this into the original system of equations, only q= works, why?
thanks