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Question

Find k for which the system kx-y=2 and 6x-2y=3 has a unique solution.

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Solution

Given system of equations are

6x2y=3

6x2y3=0 ----( 1 )

kxy=2

kxy2=0 ----( 2 )

Compare above equations with

a1x+b1y+c1=0 and

a2x+b2y+c2=0 , we get

a1=6,b1=2,c1=3 ;

a2=k,b2=1,c2=2 ;

Now ,

a1a2b1b2

[ Given they have Unique solution ]

6k21

6k2

k612

k ≠ 6/2

k ≠ 3

Therefore,

For all real values of k , except k≠ 3,

Above equations have a unique solution.


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