Tickets for a movie cost $6 for children and $9 for adults. If 84 seats were filled, and the box office revenues were $585. 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 & 84\\6 & 9 & 585\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%2084%5C%5C6%20%26%209%20%26%20585%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 84\\6 & 9 & 585\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 57\\0 & 1 & 27\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2057%5C%5C0%20%26%201%20%26%2027%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 57\\0 & 1 & 27\end{matrix}\right]")
. The number of children's tickets is 57 and the number of adult tickets is 27.