Question

Find the value of m where $k\ne m$, for which the system of equations $kx-y=2$ and $6x-2y=3$ has a unique solution.

Answer 1

Given

$kx-y=2$ .......(1)

and $kx-2=y$ ........ (2)

Put the value of $y$ from (2) in (1)

$6x-2(kx-2)=3$

$6x-2kx-4=3$

$x(6-2k)=7$

For unique solution,

$6-2k\ne 0$

$6\ne 2k$

$k\ne 3$

Comparing with $k\ne m$, we get $m=3$.