Set up a system of equations for the following scenario. then solve for the system. three students buy different combinations of tickets for a baseball game. the first student buys 2 senior, 1 adult, and 2 student tickets for $51. the second student buys 1 adult and 5 student tickets for $55. the third student buys 2 senior, 2 adult, and 7 student tickets for $75. set up a system of equations to find the price of each ticket.

Let
x =  cost of a ticket for a senior
y = cost of a ticket for an adult
z =  cost of a ticket for a student.

The first student buys 2 senior, 1 adult, and 2  student tickets for $51.
Therefore
2x + y + 2z = 51                 (1)

Th second student buys 1 adult and 5  student tickets for $5.
Therefore
y + 5z = 55                       (2)

The third student buys 2 senior, 2 adult, and 7 student tickets for $75.
Therefore
2x + 2y + 7z = 75            (3)

The system of equation for determining x, y, and z is
2x + y + 2z = 51
        y + 5z = 55
2x + 2y + 7z = 75

Warnng: The system of equations does not have a solution.