How to solve this?

"Given that integers x and y satisfying the equation 3x+5y=1. If S=x-y and S>2007, find the least possible value of S."

 

x = S + y   so  3x + 5y = 1 can be written as  3(S + y) + 5y = 1

 

Rearrange to find y in terms of S:     y = (1 - 3S)/8  This must be an integer so try values of S from 2008 onwards:

 

S           y

 

2008    -752.875    no

2009   -753.25       no

2010   -753.625     no

2011   -754            yes

 

So  S = 2011