Tickets for a movie cost $7 for children and $12 for adults. If 119 seats were filled, and the box office revenues were $1013. 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 & 119\\7 & 12 & 1013\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%20119%5C%5C7%20%26%2012%20%26%201013%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 1 & 119\\7 & 12 & 1013\end{matrix}\right]")
. Using RREF gives ![LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 83\\0 & 1 & 36\end{matrix}\right]](/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2083%5C%5C0%20%26%201%20%26%2036%5Cend%7Bmatrix%7D%5Cright%5D%20 "\displaystyle \left[\begin{matrix}1 & 0 & 83\\0 & 1 & 36\end{matrix}\right]")
. The number of children's tickets is 83 and the number of adult tickets is 36.