Question 998324
Call adult and youth tickets, x and y.
The number equation is
x + y = 728
The value equation is
19x + 8y = 10653
Multiply the first equation by 19 and subtract...
19x + 8y = 10653
-(19x + 19y = 13832)
which gives us
-11y = -3179
and
y = 289 youth tickets which gives us 
x = 728 - 289 = 439 adult tickets