Tickets for a movie cost $5 for children and $10 for adults. If 105 seats were filled, and the box office revenues were $685. 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 & 105\\5 & 10 & 685\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%20105%5C%5C5%20%26%2010%20%26%20685%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 105\\5 & 10 & 685\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 73\\0 & 1 & 32\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2073%5C%5C0%20%26%201%20%26%2032%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 73\\0 & 1 & 32\end{matrix}\right]")
. The number of children's tickets is 73 and the number of adult tickets is 32.