Q10 of 37 Page 195

y is a sum of two variables, one of which varies directly with x and another varies inversely with x. With x = - 1, then y = 1 and when x = 3, then y = 5. Let us find the relation between x and y.

Given:

y = a + b


Acc. To given condition:


a ∝ x


a = kx




Put the values of a and b in y.



x = -1 then y = 1



⇒ 1 = -k – m ….(1)


x = 3 then y = 5




⇒ 15 = 9k + 3m …(2)


Multiply (1) by 3


We get,


3 = -3k – 3m …(3)


Add (2) and (3)


18 = 6k


⇒ k = 3


Put it in (1)


1 = -3 –m


⇒ m = -4




This is the required relation between x and y.


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