Question 1019647
Sometimes it is easier to solve a math problem by brute force, especially when the values we expect to get are moderate, positive values.

By a little trial and error, a particular solution to the Diophantine equation is x = 5 and y = 15.

(BTW, A Diophantine equation ax+by = c has solutions if and only if gcd(a,b) divides c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones.)