CAT 2004 Question Paper Question 35

Question 35

The total number of integers pairs (x, y) satisfying the equation x + y = xy is

Solution

xy = x + y 

=> xy - x - y = 0

=> xy - x - y + 1 = 1

=> (x - 1) (y - 1) = 1

=> Both x - 1 and y - 1 have to be equal to 1 or -1.

So, values taken by (x,y) are (2,2) and (0,0).

=> 2 solutions



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