For the high school’s production of "grease," 490 tickets were sold. The cost of a student ticket was $8, a pre-sale non-student ticket was $10, and a ticket at the door cost $12. The total income from ticket sales was $4600. The combined number of student and pre-sale tickets was 6 times more than the tickets sold at the door. Which system of equations could be used to determine the number of each type of ticket sold?.