The pair of linear equations $2 k x + 5 y = 7, 6 x - 5 y = 11$ has a unique solution if

k \neq - 3

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k \neq 3

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k \neq 5

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k \neq - 5

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Solution

The correct option is D $k \neq - 3$
The equation are
$2 k x + 5 y - 7 = 0$
$6 x - 5 y - 11 = 0$
Here, $a_{1} = 2 k, b_{1} = 5, c_{1} = - 7$
and $a_{2} = 6, b_{2} = - 5, c_{2} = - 11$
$F o r t h e s y s t e m t o h a v e u n i q u e s o l u t i o n$
$\Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
$\Rightarrow \frac{2 k}{6} \neq \frac{5}{- 5}$
$\Rightarrow 2 k \neq - 6 \Rightarrow k \neq - 3$

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