Question

Find the no of ordered pair of (x,y) such that (7x+2y)(4x+y)=11

Answer 1

Given :   (7x+2y)(4x+y)=11    , x , y are integers

To find :   no of ordered pair of (x,y)

Solution:

x , y are integers   => 7x+2y     & 4x + y   are integers

11 =  11 *  1     or    1  *  11   or  (-11)(-1) or   (-1)(-11)

Case 1

7x+2y = 11

4x  + y = 1

=> x  = - 9  => y = 37     ( -9 , 37)

Case 2

7x+2y = 1

4x  + y = 11

=> x  = 21  => y = -73    ( 21 , -73)

Case 3

7x+2y = -11

4x  + y = -1

=> x  = 9  => y = -37     ( 9 , -37)

Case 4

7x+2y = -1

4x  + y = -11

=> x  = -21  => y = 73    ( -21 , 73)

( -21 , 73)  , ( -9 , 37) ,  ( 9 , -37) ,   ( 21 , -73)

4 ordered pairs

no of ordered pair of (x,y) such that (7x+2y)(4x+y)=11    is  4

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