For what values of $k$ does the pair of equations $x - 2 y = 3, 3 x + k y = 1$ have a unique solution? [ 2 MARKS]

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Solution

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Application : 1 Mark

Given equations are,

$x - 2 y = 3 \Rightarrow x - 2 y - 3 = 0 \dots \dots (i)$

$a_{1} = 1, b_{1} = - 2, c_{1} = 3$

$3 x + k y = 1 \Rightarrow 3 x + k y - 1 = 0 \dots \dots (i i)$

$a_{2} = 3, b_{2} = k, c_{2} = - 1$

For pair of equations to have unique solution,

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

$\frac{1}{3} \neq \frac{- 2}{k}$

$\Rightarrow k \neq - 6$

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