Final answer:
The correct system of equations representing the ticket purchases for Lin's and Mike's families is 2x + 2y = 26 for Lin's family (2 adult, 2 child tickets) and 2x + 3y = 31 for Mike's family (2 adult, 3 child tickets).
Step-by-step explanation:
The question asks to determine which system of equations represents the scenario of ticket purchases. We are given that Lin's family buys 2 adult tickets and 2 child tickets for $26, and Mike's family buys 2 adult tickets and 3 child tickets for $31. We will use 'x' to represent the cost of an adult ticket and 'y' to represent the cost of a child ticket.
The two equations to represent this situation are:
2x + 2y = 26 (Equation for Lin's family's purchase)
2x + 3y = 31 (Equation for Mike's family's purchase)
Therefore, the correct system that represents the situation is:
- Option A) 2x + 2y = 26
- Option B) 2x + 3y = 31