Find $x,y$ such that $x=4y$ and $1$-$9$ occur in $x$ or $y$ exactly once.

Question

$x$ is a $5$-digits number, while $y$ is $4$-digits number. $x=4y$, and they used up all numbers from 1 to 9. Find $x,y$.

Can someone give me some ideas please? Thank you.

Answer 1

Here are the $x,y$ pairs a quick bit of code found.

15768 3942

17568 4392

23184 5796

31824 7956

No insight to offer at the moment I'm afraid..

Answer 2

$4 \cdot 5796 = 23184$.

Lucky guess, I guess.