Question:

Find all solutions that are positive integers of the Diophantine equation:

25x + 35y = 380

I need to check my answer. Not sure If I have the correct solutions

x > 0

y > 0

25x + 35 = 380 ==> x = 13.8

25 + 35y = 380 ==> y = 10.14

0 < x < 14

0 < y < 11

25x + 35y = 380 ==> 5x + 7y = 76

25x + 175k + 105 = 380 making

x = 11-7k

25(11) + 35(4) = 275 + 105 = 380

25(4) + 35(8) = 100 + 280 = 380

Solution

K(0,1)

X(11,4)

Y (3,8)

Not sure if I expressed my answer corretly.