The general solution of the linear Diophantine equations

Find the general solution ( if solution exist) of each of the following linear Diophantine equations:

(a) 2x + 3y = 4 (d) 23x + 29y = 25
(b) 17x + 19y = 23 (e) 10x - 8y = 42
(c) 15x + 51y = 41 (f ) 121x - 88y = 572

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Solution Summary

This solution is comprised of a detailed explanation for finding the general solution ( if solution exist) of
the linear Diophantine equations.
It contains step-by-step explanation for finding the general solution ( if solution exist) of each of the
following linear Diophantine equations:

(a) 2x + 3y = 4 (d) 23x + 29y = 25
(b) 17x + 19y = 23 (e) 10x - 8y = 42
(c) 15x + 51y = 41 (f ) 121x - 88y = 572

Solution contains detailed step-by-step explanation.