Step 1 :Define two variables, \(s\) for the number of student tickets sold and \(a\) for the number of adult tickets sold.
Step 2 :Write the first equation derived from the total number of tickets sold, which is \(s + a = 98\).
Step 3 :Write the second equation derived from the total revenue, which is \(6s + 9a = 747\).
Step 4 :The system of equations is: \[s + a = 98\] \[6s + 9a = 747\]
Step 5 :Solve the system of equations to find the values of \(s\) and \(a\).
Step 6 :The solution is \(a = 53, s = 45\).
Step 7 :Final Answer: The number of adult tickets sold is \(\boxed{53}\) and the number of student tickets sold is \(\boxed{45}\).