Hi everyone!

I have my own comfortable way of solving equations with two unknowns like:

5s + 42t = 1

What I do when I solve this equation, is that I first think: ok, the absolute value of s must be bigger than the absolute value of t in order to get an answer as close to 1 as possible. Than I try t = 1, t = 2... and test with the appropriate s in order to get an answer as close to 1 as possible. The problem is that my method becomes extremely long for big numbers such as

123 456 s + 654 321 t = 3

Does anyone perhaps know some easy to use, good method which would solve these kind of equations efficiently?

Thank you all so much for reading this!