Linear Diophantine Equations

#1

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In this simplification, I was confused about when substituting a and b as gk1 and gk2, where does the y term go. I’m not able to understand how the equation is solved past deciding the values to substitute for a and b.

#2

hello @singh_04
y should be there only.
bhaiya have missed it by mistake

#3

can you then solve the remaining proof as I’m unable to understand ahead from that

#4 
Ax+By=C
K1gx+K2gy=c
K1x+K2y=c/g

Everything after this was correct