Tickets for a movie cost $6 for children and $11 for adults. If 107 seats were filled, and the box office revenues were $817. 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 & 107\\6 & 11 & 817\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%20107%5C%5C6%20%26%2011%20%26%20817%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 107\\6 & 11 & 817\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 72\\0 & 1 & 35\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2072%5C%5C0%20%26%201%20%26%2035%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 72\\0 & 1 & 35\end{matrix}\right]")
. The number of children's tickets is 72 and the number of adult tickets is 35.