If $17x+51y=85$, find the value of $19x+57y$
I know I could use substitution and figure this out but i wanted to use Diophantine equation. I'm just a little confused because I know that $\gcd(17,51)=17$ and $17|85$
I could use the extended EA to get that a particular solution is $x_0 =5$ and $y_0=0$
The complete solution is $x=5+51n$ and $y=0-17n$
Not sure where to go from here.
Also I know how to do the EA, I just didn't want to write out all the steps so I just put it into a EA calculator. I'm just a little confused on how to get the solutions for $19x+57y$