Finite math problem about finding values

Question

Given that 2 sheep, 3 dogs, 6 hens, and 3 rabbits cost 883 coins, 5 sheep, 2 dogs, 4 hens, and 4 rabbits cost 1286 coins, 3 sheep, 1 dog, 3 hens, and 5 rabbits cost 833 coins, 4 sheep, 5 dogs, 5 hens, and 1 rabbit cost 1365 coins, how much does each animal cost?

Answer 1

We can solve this set of linear equations using linear algebra such that Ax= b

We can set up a matrix, A, such that of the number of each animal:

A =

2 3 6 3
5 2 4 4
3 1 3 5
4 5 5 1

We can also give a vector, b, of the total cost of each combination:

 

b =

883
1286
833
1365

Therefore the cost of each animal will be give by the vector x such that:
x =

s = 176.0000
d = 103.0000
h = 24.0000
r  = 26.0000