## Quant Question Of The Day: 232

**Total number of integers pairs (x,y) that satisfy the equation**

**4x+3y = 3xy**

**2****3****1****infinite many**

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**Total number of integers pairs (x,y) that satisfy the equation**

**4x+3y = 3xy**

**2****3****1****infinite many**

**Anwer: (2) 3 pairs**

**Solution**

**3xy-4x = 3y**

**x= 3y/(3y-4)**

**x= 1+ 4/(3y-4)**

**now x will be integer when 3y-4 is a factor of 4 (both positive and negative values)**

**hence 3y-4 = 1 , 2 , 4 , -1, -2 , -4 **

**y will be 5/3, 2, 8/3, 1, 2/3, 0 **

**hence y will be integer on 3 of those values.**

**Hence there are 3 integer pairs of (x,y) that satisfy the above equation.**

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