Formulate a system of equations for the situation below and solve.

For the opening night at the Opera House, a total of 1000 tickets were sold. Front orchestra seats cost $100 apiece, rear orchestra seats cost $80 apiece, and front balcony seats cost $70 apiece. The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by 400. The total receipts for the performance were $84,400. Determine how many tickets of each type were sold.