If you have 36 total animals and 100 total legs, and each dog has 4 legs and each chicken has 2 legs, you can use a system of linear equations to find the exact number of dogs and chickens.
Let x be the number of dogs and y be the number of chickens.
x + y = 36 (total number of animals)
4x + 2y = 100 (total number of legs)
Solve for x in the first equation: x = 36 - y
Substitute this expression for x in the second equation:
4(36 - y) + 2y = 100
Expand and simplify:
144 - 4y + 2y = 100
144 - 2y = 100
Subtract 100 from both sides:
44 = -2y
Divide both sides by -2:
y = -22
So, there are -22 chickens, which is not possible. This means that the initial assumption that the number of legs is 100 is incorrect.
