g = number of tickets for goldfish
t = number of tickets for tacky mirrors
s = number of tickets for stuffed tiger
1g + 2t + 1s = 40
5g + + 1s = 40
2g + 3t = 40
using the second equatin we can find a value for s
1s = 40 -5g
now substitute in the first equation to get rid of s
1g + 2t + (40-5g) = 40
-4g + 2t = 0
now use this new equation with equation 3 and solve for one of the values
-4g + 2t = 0
2g + 3t = 40
multipy the second equation by 2 and then combine
-4g + 2t = 0
4g + 6t = 80
8t = 80
t = 10 (so it takes 10 tickets to get a takcy mirror)
2g + 3(10) = 40
2g = 10
g = 5 (five tickets to get a goldfish)
s = 40 -5(5)
s = 15 (fifteen tickets for a stuffed tiger)
1(5) + 2(10) + 1(15) (substitute back in the first equation)
5 + 20 + 15
40 it works!
