Question

In a rectangular coordinate plane, which quadrant, if any, contains no point (x,y) such that it satisfies the inequality 2x-3y<-6

Answer 1

Given :  inequality 2x-3y<-6

To find :  which quadrant, if any, contains no point (x,y) satisfying inequality

Solution:

2x  -  3y  <  - 6

at  x  =  0

=> - 3y  < - 6

=>  y  >  2  

x = 1    => y > 8/3  ( hence 1st Quadrant - point lies)

x = - 1  => y > 4/3

x =  - 3  y >  0      ( hence 2nd  Quadrant - point lies)

x = - 6  

=> y > - 2           ( hence 3rd  Quadrant - point lies)

but if   y   <  0

then    x  <  0    ( hence 4th Quadrant not possible)

where x is + Ve    &  y  is - ve

4th Quadrant does not contain any points  

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