No, you can’t throw him out of your house. He is very young and won’t be able to make it on his own. On the other hand he needs to be in some sort of framework/program where he is accomplishing a goal. It is more than okay for you to discuss goals with him like getting a job and moving out eventually.
I understand your situation very well as I went through it. there are good times and sometimes very BAD times. Thank G-d my daughter had her own room, it would have been very hard if she was sharing a room with a sibling. I tried making rules in the house but she had a hard time following and did what she pleased. It was hard for all of us.