turkeys and chickens

Question

it takes 8 turkeys and 12 chickens 10 hours to eat a certain amount of grain, while it takes 6 turkeys and 8 chickens 14 hours to eat the same amount of grain. find the time it takes 1 turkey alone and 1 chicken alone to eat the same amount of grain.

Answer 1

8t + 12c = 10

6t + 8c = 14

divides by 2:

4t + 6c = 5

3t + 4c = 7

solves by elimination

12t + 18c = 15

-12t + -16c = -28

2c = -13

c = -13/2

3t + 4(-13/2) = 7

3t - 26 = 7

3t = 33

t = 11