find the gneeral solution of the linear diophantine equation

find the gneeral solution of the linear diophantine equation 2x+3y=4

Solution

Since the gcd(2,3) = 1

3 = 2 * 1 + 1

2 = 1 * 2 + 0

1 = 3 - 2*1

Hence the initial solution will be (2,0), hence the after wards solution are (2+3t) and (-2t)