Tickets at the theater or $9 for adults seniors receive a discount and only have to pay $6 but capicity of the theater is 80 people. if the theater was at full capacity and made $675, then how many seniors bought tickets for the movies? and how did you get that answer

So $9 for adults and $6 for seniors

so number of adults is represented by x
number of seinors is represented by y

9x+6y=675 since every adult pays 9 and seinors pay 6

x+y=80 since adults+seinors=80

multiply x+y=80 by -6
-6x-6y=-480
add this to 9x+6y=675
9x-6x+6y-6y=675-480
3x+0=195
divide both sides by 3
x=65
there were 65 adults

subsitute 65 for x in x+y=80
65+y=80
subtract 65 from both sides
y=15

there were 15 seinors at the event