[tex]x-\ number\ of\ adult\ tickets\\\\
y-\ number\ of\ children\ tickets\\\\
x+y=24\ \ \ \ | x=24-y\\\\
x*5,5+2*y=83\\\\
5,5(24-y)+2y=83\\\\132-5,5y+2y=83\\\\
132-3,5y=83\ \ \ \ | subtract\ 132\\\\
-3,5y=-49\ \ \ | divide\ by\ -3,5\\\\y=14\\\\
x=10\\\\
He\ bought\ 10\ adult\ tickets\ and\ 14\ children\ tickets.
[/tex]
