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

Given: The system of equations $kx-y=2$ and $6x-2y=3$.

To do: To find the value of $k$ for which the system of equations has a unique solution.

Solution:

The given system is  

$kx-y-2=0\ .....( i)$  

$6x-2y-3=0\ ....( ii)$  

Here, $a_1 = k,\ b_1 = -1,\ c_1 = -2,\ a_2 = 6,\ b_2 = -2$ and $c_2 = -3$

For the system, to have a unique solution, we must have:

$\frac{a_1}{a_2}≠\frac{b_1}{b_2}$

$\Rightarrow \frac{k}{6}≠\frac{-1}{-2}$

$\Rightarrow -2k≠-6$

$\Rightarrow k≠\frac{-6}{-2}$

$\Rightarrow k≠3$

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Updated on: 10-Oct-2022

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