Tickets for a movie cost $5 for children and $10 for adults. If 120 seats were filled, and the box office revenues were $700. 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 & 120\\5 & 10 & 700\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%20120%5C%5C5%20%26%2010%20%26%20700%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 120\\5 & 10 & 700\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 100\\0 & 1 & 20\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%20100%5C%5C0%20%26%201%20%26%2020%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 100\\0 & 1 & 20\end{matrix}\right]")
. The number of children's tickets is 100 and the number of adult tickets is 20.