What would you feel if you entered on your guy going at another woman?

Her moving with me has been more of a "deal". After seeing her for a few weeks, I suggested she stays at my place cause I needed someone to keep the home tidy and make the occasional meal, and also it's not far from her beauty school, which is what she does. And so she stays with me while I cover the home's expenses etc. And I got a girl around the house. And I like her, and have no intention of dumping her. So yeah technically it is a relationship. I just don't know if me cheating would ruin all of that. I might just do the thing you suggested.