A car rental agency rents compact, midsize, and luxury cars. Its goal is to purchase 70 cars with a total of $1,200,000 and to earn a daily rental of $3000 from all the cars. The compact cars cost $10,000 and earn $30 per day in rental, the midsize cars cost $20,000 and earn $50 per day, and the luxury cars cost $40,000 and earn $80 per day. To find the number of each type of car the agency should purchase, solve the system of equations below, where x, y, and z are the numbers of compact cars, midsize cars, and luxury cars, respectively.