4. (20 points) For the opening night at the Opera House, a total of 1000 tickets were sold. Front orchestra seats cost $80 apiece, rear orchestra seats cost $60 apiece, and front balcony seats cost $50 apiece. The combined number of tickets sold for the front orchestra and rear orchestra was twice the number of front balcony tickets sold. The total receipts for the performance were $62,800. Formulate, but do not solve, a system of equations to determine how many tickets of each type were sold. Let x,y, and z represent the number of front orchestra, rear orchestra, and front balcony tickets, respectively