hmm...i think....that you should prove first that every homomorphic image of a solvable group is solvable. then find a group with two generators that isn't solvable.
ok, suppose you know the homomorphic image of a solvable group is solvable. suppose you find a group with 2 generators that ISN'T solvable.
isn't such a group a quotient group of the free group on two generators? and aren't quotient groups of a group just homomorphic images of that group
(the first isomorphism theorem)?