Tickets for a movie cost $7 for children and $10 for adults. If 86 seats were filled, and the box office revenues were $683. 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 & 86\\7 & 10 & 683\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%2086%5C%5C7%20%26%2010%20%26%20683%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 86\\7 & 10 & 683\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 59\\0 & 1 & 27\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2059%5C%5C0%20%26%201%20%26%2027%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 59\\0 & 1 & 27\end{matrix}\right]")
. The number of children's tickets is 59 and the number of adult tickets is 27.