Tickets for a movie cost $5 for children and $11 for adults. If 129 seats were filled, and the box office revenues were $849. 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 & 129\\5 & 11 & 849\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%20129%5C%5C5%20%26%2011%20%26%20849%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 129\\5 & 11 & 849\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 95\\0 & 1 & 34\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2095%5C%5C0%20%26%201%20%26%2034%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 95\\0 & 1 & 34\end{matrix}\right]")
. The number of children's tickets is 95 and the number of adult tickets is 34.