For what value of $k$ the following pair of the linear equation has a unique solution ?
$x - k y = 2, 3 x + 2 y = - 5$

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Solution

$x - k y = 2$
$3 x + 2 y = - 5$
Unique Solution
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
$\frac{1}{3} \neq \frac{- k}{2}$
$- 3 k \neq 2$
$k \neq - \frac{2}{3}$
For unique real value of $k$ except $\frac{- 2}{3}$

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Find the value for k which each of the following systems of equations has a unique solution:

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