Find k for which the system kx-y=2 and 6x-2y=3 has a unique solution.
Given system of equations are
6x−2y=3
6x−2y−3=0 ----( 1 )
kx−y=2
kx−y−2=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 ,
a1a2≠b1b2
[ Given they have Unique solution ]
6k≠−2−1
6k≠2
k6≠12
k ≠ 6/2
k ≠ 3
Therefore,
For all real values of k , except k≠ 3,
Above equations have a unique solution.