Question 1160221
chickens have 2 legs.
rabbits have 4.
chickens and rabbits have 1 head each.
let x = the number of chickens.
let y = the number of rabbits.
x + y = 70 is the equation for the total number of heads.
2x + 4y = 196 is the equation for the total number of legs.
these 2 equations need to be solved simultaneously to find out how many chickens and how many rabbits.
multiply both sides of the first equation by 2 and leave the second equation as is to get:
2x + 2y = 140
2x + 4y = 196
subtract the first equation from the second to get:
2y = 56
solve for y to get:
y = 56/2 = 28
since x + y = 70, then x must be equal to 70 - 28 = 42
you have 42 chickens and 28 rabbits.
they each have 1 head, so x + y = 70 becomes 42 + 28 = 70 which is confirmed to be correct.
each chicken has 2 legs and each rabbit has 4 legs, so 2x + 4y = 196 becomes 42 * 2 + 28 * 4 = 84 + 112 = 196 is also confirmed to be correct.
your solution is that there are 42 chickens and 28 rabbits on the farm.