How do I find two different integer solutions of 299a + 247b = 13

I can find them using guess and check, I got one set of solutions a = 5 and b = -6
But I don't know an easy way to find other solutions, or even better, the set of all integer solutions.

These are linear diophantine equations go look them up, theyre quite interesting
Given that ax+by = n
It only has integer solutions if (a,b) is a factor of n.
There are infinite solutions moreso they are in the form
a = 19n+5 and b = -23n-6
Plug in any number for a solution

To solve this, first you want to solve it mod 13. And you'll quickly note that 299 and 247 are both divisible by 13, so you can reduce this equation to:

23a + 19b = 1

Now, we need a number a such that 23a === 1 mod 19. Once you have that, you can produce a general solution to the equation:

23 * 5 = 115 === 1 mod 19.

So you can use a = 19n + 5, and when you plug that in you get b=19n-6. This generates all solutions.