Thomas was selling tickets to his school play. The tickets cost $5.00 for adults and $2.00 for children. He sold 200 tickets and collected $610. Which system represents the number of adult and child tickets that Thomas sold?

Adult: $5, qty x

children: $2, qty y

total: $610, qty 200

Cost: 5x + 2y = 610

Quantity: x + y = 200

Using elimination method to solve the system of equations:

1 (5x + 2y = 610) → 5x + 2y = 610

-2 (x + y = 200) → - 2x - 2y = - 400

Add both equations: 3x + 0 = 210

Divide both sides by 3: x = 70

Substitute "x = 70" into either the Cost or Quantity equation:

Quantity: x + y = 200 → 70 + y = 200 → y = 130

Adult tickets sold = 70

Children tickets sold = 130