Forwarding a website without changing the visible URL

I would like to forward users who visit xyz.com to abc.com/xyz without the URL changing, and without using an iframe. I also want xyz.com/1 to lead to abc.com/xyz/1

Can you help me do this?

Other details:

1. The website at abc.com/xyz is a Wordpress site, so I can change the URL to look like xyz.com
2. The main reason for this is that getting hosting on xyz.com is way too expensive for my organization, and abc.com is owned by our parent org which gave us that options