elementary number theory - Why is it true that if $ax+by=d$ then $gcd(a,b)$ divides $d$?

Can someone help me understand this statement:

If $ax+by=d$ then $\gcd(a,b)$ divides $d$.

Bezout's identity states that:

the greatest common divisor $d$ is the smallest positive integer that can be written as $ax + by$

However the definition of $\gcd(a, b)$ is the largest positive integer which divides both $a$ and $b$.

I'm am completely lost.
If anyone could provide some sort of layout to help me sort this out I would be really happy.