Tickets for a movie cost $5 for children and $12 for adults. If 97 seats were filled, and the box office revenues were $744. How many children's and now many adult tickets were sold?
Let 
be the number of children's tickets and 
be the number of adult tickets. This gives the system of equations
. Writing the system as a matrix gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 1 & 97\\5 & 12 & 744\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%2097%5C%5C5%20%26%2012%20%26%20744%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 97\\5 & 12 & 744\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 60\\0 & 1 & 37\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2060%5C%5C0%20%26%201%20%26%2037%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 60\\0 & 1 & 37\end{matrix}\right]")
. The number of children's tickets is 60 and the number of adult tickets is 37.