Finding an inexpensive Homestay in Korea?

So I have a problem. Forever now I have been planning on going to Korea at the end of August but with little time left, I STILL haven't been able to find an inexpensive homestay in Seoul or anywhere close. I just graduated from high school and I'm using the money I've worked for and it's completely out of my own pocket. I was hoping to find a safe homestay where I could teach english to any of the family members and trade that and housework or running errands for room and board. EVEN JUST ROOM. I know it is alot to ask but there are other programs for other countries that do that exact same thing. I have looked forever on many different websites including the most popular HomestayKorea but I can't afford that. I really need help. What is there to do?