A business has three machines that manufacture containers. Together they can make 100 containers per day, whereas the two fastest machines can make 80 containers per day. The fastest machine makes 34 more containers per day than the slowest machine. 

(a) Let x, y, and be the numbers of containers that the machines make from fastest to slowest. Write a system of three equations whose solution gives the number of containers each machine can make. 

(b) Solve the system of equations.