Question 684844
20x+13y=7822
x+y=515
x is the number of adults that went to the play and y is the number of seniors that went to the play. 
Take your second equation and solve for y:
y=515-x
then substitute what your found for y into the first equation's y:
20x+13(515-x)=7822
20x+6695-13x=7822
7x+6695=7822
7x=1127
x=161
Then plug in 161 for x into your second equation to find y:
161+y=515
y=354
Then to double check plug in 354 for y in your first equation to find x:
20x+13(354)=7822
20x+4602=7822
20x=3220
x=161 (It worked!!)
161 adults went, and 354 seniors went to the play.
I hope this helps :)