number theory - Is there an integer z such that $255zequiv 7pmod {633}$?

I used the extended euclidean algorithm to

"Find integers x and y such that $633x + 255y = 6$, or explain why none exist."

And found that $6x = -58$ and $y = 144$. Now I'm stuck on the follow up question in the title. How do I proceed to answer a question like this?

Thanks

Answer

Note that $255=3\times85$ and that $633=3\times211$. As such $255z\pmod{633}$ will always be a multiple of $3$. As $7$ is not a multiple of $3$ then there is no solution.