Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 104. Two adults and three children must pay $ 73. Find the price of the​ adult's ticket and the price of a​ child's ticket.

An adult ticket is $20 and a child ticket is $11.

Our system of equations would be:

3A + 4C = 104
2A + 3C = 73

We want the coefficients of one of these variables to be the same in order to eliminate it; we will multiply the top equation by 2 and the bottom equation by 3:
2(3A + 4C = 104)
3(2A + 3C = 73)

6A + 8C = 208
6A + 9C = 219

Subtract the bottom equation:

6A + 8C = 208
-(6A + 9C = 219)

-1C = -11

Divide both sides by -1:
-1C/-1 = -11/-1
C = 11

Substitute this into the first equation:
3A + 4(11) = 104
3A + 44 = 104

Subtract 44 from both sides:
3A + 44 - 44 = 104 - 44
3A = 60

Divide both sides by 3:
3A/3 = 60/3
A = 20