how do you solve this in linear combination

Question

robs school is selling tickets to a choral performance on the first day of ticket sales the school sold 6 adult tickets and 2 child tickets for a total of $78. the school took in $84 on the second day by selling 3 adult tickets and 6 child tickets. what is the price each of one adult ticket and child ticket?

Answer 1

Let x = price of adult ticket and y=price of child ticket, set up a system of 2 equations in 2 variables:

 

6x + 2y = 78

3x + 6y = 84  solve via elimination (multiply 2nd equation by -2)

 

 6x +  2y = 78

-6x - 12y = -168  add them together and solve for y

 

-10y = -90

y = 9  substitute to find x

 

6x +18 = 78

6x = 60

x = 10