Question

Can anyone solve the question number 2 for me?

Answer 1

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Answer 2

Given : 99x + 101y = 499xy    ------ (1)

Given : 101x + 99y = 501xy    ------ (2)

On adding (1) & (2), we get

⇒ 200x + 200y = 1000xy

⇒ x + y = 5xy

On subtracting (1) & (2), we get

⇒ 99x + 101y - 101x - 99y = 499xy - 501xy

⇒ -2x + 2y = -2xy

⇒ x - y = xy  

On solving both equations, we get

⇒ x + y = 5xy

⇒ x - y = xy

   -----------------

  2x = 6xy

    y = 1/3

Substitute x = (1/3) in above equations, we get

⇒ x - y = xy

⇒ x - (1/3) = x * (1/3)

⇒ x = (1/3)x + 1/3

⇒ 2x = 1

⇒ x = 1/2.

Therefore, the value of x = 1/2 and y = 1/3.

Hope this helps!