# Solutions of Linear Diophantine Equation ax + by = c

If (xo,yo) is a solution of the Linear Diophantine equation ax + by = c , then the set of solutions of the equation consists of all integer pairs (x,y), where either x = xo + tb/d and y = yo - ta/d ( t = ........,-2,-1,0,1,2,........)

or , x = xo - tb/d and y = yo + ta/d ( t = .........,-2,-1,0,1,2,.......) where d = g.c.d.(a,b).

https://brainmass.com/math/basic-algebra/solutions-of-linear-diophantine-equation-ax-by-c-23557

#### Solution Summary

This solution is comprised of a detailed explanation for the Linear Diophantine Equation.

It contains step-by-step explanation for if (xo,yo) is a solution of the Linear Diophantine equation ax + by = c ,

then the set of solutions of the equation consists of all integer pairs (x,y), where

either x = xo + tb/d and y = yo - ta/d ( t = ........,-2,-1,0,1,2,........)

or , x = xo - tb/d and y = yo + ta/d ( t = .........,-2,-1,0,1,2,.......) where d = g.c.d.(a,b).

Solution contains detailed step-by-step explanation.