In a zoo, there are Rabbits and Pigeons. If heads are counted, there are 200 and if legs are counted, there are 580. How many pigeons are there?

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The simplest Way is -

Total No of 4 Leg Animal(Rabbit ) = ((Total no of legs/2) -No. of heads)
Rabbit = 580/2 - 200
Rabbit = 90
Pigeon = 200 - 90 = 110

Let rabbit =x
Pegion =200-x

4x(because rabbit has 4 legs)+2(200-x)=580
400+2x=580
2x=180
X=90

Rabbit =90
Pegion=110ans.

Try to improve your solutions. Make it understandable.
Comment section helped me in this question.

Let pigeons= X
Rabbits = y
X+Y= 200 ......(1)
2X+4Y =580 .... (2)
Then
4X + 4Y = 800
2X + 4Y = 580
- - -
------------------
2X = 220
X = 110

Let pigeons= X
Rabbits = y
X+Y= 200 ......(1)
2X+4Y =580 .... (2)
Then
4X + 4Y = 800
2X + 2Y = 580
- - -
------------------
2X = 220
X = 110

Assuming that all are pigeons then total pigeons leg count will be 200*2(legs) = 400 legs.
and all are Rabbits then total Rabbit's leg count will be 200*4(legs) = 800 legs.
400 800
/
580(Given)
/
800-580 580-400
=220 =180
Ratio =11:9
Ratio Sum 11+9=20
which is given as 200
So 11 parts will be 11×20020
=110 Piegons.

Nt understood

Let no of rabbits be x
pigeons be y
x+y=200 ..... (1)
Now, rabbits have 4 legs, whereas pigeons have 2 legs
so, 4x+2y= 580 .... (2)
W
on solving eq 1 and 2
we will get y=110

(pigeons+rabbits)=200 (by heads)
let the nos of pigeons =x
then the nos of Rabbits = 200-x
now total no of feets =2*nos of pigeons+4*nos of rabbits
580 = x*2+4*(200-x)
2x+800-4x=580
-2x=-220
x=220/2=110
2x=220
x=110

not understand