Write the value of k for which the system of equations x + ky = 0, 2x − y = 0 has unique solution.

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Solution

The given equations are

$x + k y = 0 2 x - y = 0 a_{1} = 1, a_{2} = 2, b_{1} = k, b_{2} = - 1 \frac{a_{1}}{a_{2}} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{k}{- 1}$
For unique solution

For all real values of k, except the equations have unique solutions.

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