The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. What is the price each of senior citizen ticket and one student ticket?

Let:

x = cost of senior citizen ticket

y = cost of student ticket

4x + 5y = 102

7x + 5y = 126

4x + 5y = 102

4x = 102 - 5y

x = (102 - 5y) / 4

x = 102/4 - 5y/4

7x + 5y = 126

7 (102/4 - 5y/4) + 5y = 126

(714/4 - 35y/4) + 5y = 126

-35y/4 + 5y = 126 - 714/4

note:

-35y/4 = - 8.75y

714/4 = 178.5

-8.75y + 5y = 126 - 178.5

-3.75y = - 52.5

y = - 52.5/-3.75

y = 14

x = 102/4 - 5y/4

x = 102/4 - 5 (14) / 4

x = 8

x = cost of senior citizen ticket = $8/ea

y = cost of student ticket = $14/ea