Find whole numbers $x$ and $y$ such that $61=9x+15y$

Question

Do whole numbers $x$ and $y$ exist so 61 can be written in the form $61=9x+15y$?

My book just covered Bezout's identity. How can I use it to find out if the coefficients exist?

Answer 1

$\gcd(9,15) = 3$

Since $3$ does not divide $61$, no such numbers can be found.

Answer 2

Hint: The right hand side is always divisible by _____ no matter what integers $x$ and $y$ you pick.