LinearDiophantineEq
 

LinearDiophantineEq: will solve equation a*x+b*y=c
where x and y are integers, nothing special about it.

https://www.techiedelight.com/find-general-solution-linear-diophantine-equation/
https://raw.githubusercontent.com/wandering007/algorithms/master/extended_gcd.cpp

Implied, but maybe not obvious that it's more restrictive than that - all four left hand variables muct be integers.

Git

a, b, c must be also be integers.

One may ask what if x and y are not integers but real numbers,
then we will have an infinite number of solutions:
for each x value there is a y value
and for each y value there is a x value,
which is another way of saying we don't have enough information about x and y from a single equation.