(In reply to Simplified, no solution
Even though Jer's simplification significantly reduces the burden of solving analytically, one will still be left with 95 simple sets of equations like:
(i) y+z =k k<95,
(ii) G = 2y + 5*(k-y) each set creating a subset of possible G,
then creating the union of various solutions to avoid duplicity and then returning to linear translation to get H.
Clearly, this is a proper puzzle for a heuristic exhaustive program and any shortcuts are not needed.