Abhay's Math
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Derivation of General Formula
Let p,q,w,x,y,z,T be known integers and a,b,c,d be unknown integers and the equation be :
pab + qcd = wa + xb + yc + zd + T
pa(b - w/p) + qc(d - y/q) = xb + zd + T
pa(b - w/p) + qc(d - y/q) = x(b - w/p + w/p) + z(d - y/q + y/q) + T
(b - w/p)(pa - x) + (d - y/q)(qc - z) = wx/p + yz/q + T
Multiplying both sides by pq
q(pb - w)(pa - x) + p(qd - y)(qc - z) = qwx + pyz + Tpq
This result may be learnt. It will become easier to memorise after seeing illustrations.
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