The arcadia theater charges $8 for adult tickets and $2 for student tickets. mr. steele purchased 9 tickets (some student and some adult) for $30. which system of equations could be used to find a, the number of adult tickets, and s, the number of student tickets mr. steele purchased?

let [tex]a[/tex] be the adults, and let [tex]s[/tex] the number of students.
We know for our problem that Mr. Steele purchased 9 tickets, so [tex]a+s=9[/tex]. This is first equation of our system of equations.
We also know that the Arcadia theater charges $8 for adult tickets and $2 for student tickets, so [tex]8a+2s=30[/tex]. This is the second equation of our system.

Now, lets put both equations together to create the system of equation that could be used to find a, the number of adult tickets, and s, the number of student tickets Mr. Steele purchased:
[tex] \left \{ {{a+s=9} \atop {8a+2s=30}} \right. [/tex] 

To solve our system, we are going to solve for [tex]a[/tex] in equation (1), and then we are going to replace that value in equation (2):
From equation (1):
[tex]a=9-s[/tex] equation (3)
Replace equation (3) in equation (2):
[tex]8(9-s)+2s=30[/tex]
[tex]72-8s+2s=30[/tex]
[tex]-6s=-42[/tex]
[tex]s= \frac{-42}{-6} [/tex]
[tex]s=7[/tex] equation (4)
Replace equation (4) in equation (3):
[tex]a=9-7[/tex]
[tex]a=2[/tex]

We can conclude that Mr. Steele purchased 2 adult tickets and 7 student tickets.