The matrix representation for the given system of equations is:
[tex]\left[\begin{array}{cc}1&1\\9&12\end{array}\right] \left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}820\\9222\end{array}\right][/tex]
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable x: Number of children tickets sold.
- Variable y: Number of adult tickets sold.
On Friday, the theater sold 820 tickets total, hence:
x + y = 820.
At a movie theater, the price of a child's ticket is $9 and the price of an adult's ticket is $12. The theater made $9,222, hence:
9x + 12y = 9222.
Then the matrix representation for the system is:
[tex]\left[\begin{array}{cc}1&1\\9&12\end{array}\right] \left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}820\\9222\end{array}\right][/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
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