Set up a system of equations describing the following word problem. Be sure to specify what each variable represents.
A private school spent $860,000 in one year to pay all of its teachers and administrators. The school has a total of twenty-four teachers and administrators combined. If teachers make $35,000 per year and administrators make $40,000 per year, how many teachers and how many administrators does the school have? Also, where in the country do these people live that they are able to get by on such a pittance? You hear that, private school? We're calling you out.