Your problem states that

people attended the theater that day, grossing

, at

per ticket per adult (

)and

per ticket per child (

). This means that

times

, the number of adults, plus

times

, the number of children, produced

, and that the total number of adults,

, plus children,

, was

. This is your system of linear equations:

You mentioned that you needed to use matrices to solve the problem. Then you will need to convert your system of linear equations to matrix form, as follows:

This will produce a matrix equation of the form

for:

such that:

Given

and

, you need to find

, the inverse matrix of

, if it exists, to solve the equation. Using elementary row operations on

, the augmented matrix of

, allows you to obtain

:

So that:

Since

for:

then:

Therefore,

adults and

children attended the theater that day.