(In reply to

Simplified, no solution by Jer)

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.