A group of friends visited the national zoological park, Delhi and at a particular time, they
observe that there are 100 legs and 72 eyes which they can view. They could recognise that
the legs and eyes they viewed were of tigers and parrots. One of them used the variables x
and y to represent the number of tigers and parrots respectively in the zoological park.
Then, another person formulated the linear equation for the total number of eyes they could
view as x + y = 6K. One more linear equation is formed for the number of legs as
2x + y = 50.
Based on the above information, answer the following questions:
(i) For what value of k will the point (8, 22) be the solution for equation of number of eyes?

(ii) How many solutions does the equation representing the number of legs have?
(iii) If k = 6 in the equation representing the number of eyes, then check if the points
(4, 32) and (21, 15) lie on the line or not.
OR
(iii) Write two solutions for the number of legs.

Solution: 
(i) Given: (8, 22) is the solution for the equation of the number of eyes, therefore, (8, 22) is the solution of x + y = 6K.

8+22=6k6k=30k=5

So, the value of k is 5.

(ii) A linear equation in two variables can have infinitely many solutions.
So,  the equation representing the number of legs have infinitely many solutions.

(iii) If k = 6, then the equation representing the number of eyes will be
x + y = 36
(4, 32) and (21, 15) satisfy the equation, so, they lie on the line.

OR

The equation representing the number of legs is 2x + y = 50.

For x = 0, 

2(0) + y = 50
⇒ y = 50

For y = 0, 

2(x) + 0 = 50
⇒ x = 25

So, (0, 50) and (25, 0) are two solutions for the equation of legs.

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