The lee’s spend $31 on movies tickets for 2 adult and 3 children. the smith’s spent $26 on movie tickets for 2 adults and 2 children. what are the prices for an adult and child movie ticket?

First we write the variables:
 x: cost of the ticket for adults.
 y: cost of ticket for children.
 We write the system of equations:
 2x + 3y = 31
 2x + 2y = 26
 We solve the system:
 Step 1:
 2x + 3y = 31
 -2x-2y = -26
 Step 2:
 y = 5
 Step 3:
 2x + 3y = 31
 2x = -3y + 31
 x = (- 3y + 31) / 2
 x = (- 3 * (5) +31) / 2
 x = 8
 
 the prices for an adult and child movie ticket are:
 adults = $ 8
 children = 5 $