[tex]x-\ amount\ of\ children\\
y-\ amount\ of\ adults\\\\
\left \{ {{x+y=2200\ \ |*(-4)} \atop {1,5x+4y=5050}} \right.\\\\ \left \{ {{-4x-4y=-8800} \atop {1,5x+4y=5050}} \right.\\\\ +-------\\
-2,5x=-3750\ \ |Divide\ by\ -2,5\\
x=1500\\
y=2200-1500\\
y=700\\\\There\ were\ 1500\ children\ and\ 700\ adults.[/tex]