Question

Find all positive integer solutions for 13x + 9y = 190 using Diophantine equations.

Answer 1

here is the same kind of question, perhaps it helps

http://www.jiskha.com/display.cgi?id=1317362332

Answer 2

1--13x + 9y = 190
2--Dividing by the lowest coefficient
...y + x + 4x/9 = 21 + 1/9
3--(4x - 1)/9 must be an integer.
4--Needing a unit coefficient
...(28x - 7)/9 = 3x + x/9 - 7/9
5--(x - 7)/9 must be an integer k making x = 9k + 7
6--Substituting back into (1) yields
---y = 11 - 13k
7--k must be '0' making x = 7 and y = 11
8--Checking, 13(7) + 9(11) = 91 + 99 = 190.