A sum of $10,000 is invested in three accounts that pay 3%, 4%, and 5% interest. Twice as much money is invested in the account paying 5% as in the account paying 3%, and the total annual interest from all three accounts is $421. 

(a) Write a system of equations whose solution gives the amount invested in each account. Be sure to state what each variable represents. 

(b) Solve the system of equations.