Find the value of k for which the system:
kx + 2y = 5, 3x + y = 1 has a unique solution

k = 6

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k \neq 9

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k \neq 6

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k = 6

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None of these

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Solution

The correct option is C $k \neq 6$
We have, kx + 2y = 5 ...... (1)
3x + y = 1 ...... (2)
Here, $a_{1} = k, b_{1} = 2, c_{1} = 5$
$a_{2} = 3, b_{2} = 1, c_{2} = 1$
The given system of equations will have a unique solution
if $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ i.e., if, $\frac{k}{3} \neq \frac{2}{1}$
i.e., if $\frac{k}{3} \neq 2$ i.e., if $k \neq 6$

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