Find the value of k for which the system of equations 2x + ky = 1, 3x - y = 7 has a unique solution.

k = - \frac{2}{3}

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k \neq \frac{2}{3}

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

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k = \frac{2}{3}

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None of these

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Solution

The correct option is C $k \neq - \frac{2}{3}$
For a unique solution to exist, we require
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \Rightarrow \frac{2}{3} \neq \frac{k}{- 1}$ , i.e., $k \neq - \frac{2}{3}$

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