Find the value(s) of $k$ so that the pair of equations $x + 2 y = 5$ and $3 x + k y + 15 = 0$ has a unique solution.

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Solution

Hint: $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Concept Used: condition to find the unique solution of the equation.
Finding the value of $k$ ,
Here, $a_{1} = 1, a_{2} = 3, b_{1} = 2, b_{2} = k$ .
$\frac{1}{3} \neq \frac{2}{k} k \neq 6$
Hence, except the value at $k = 6$ , the equations have a unique solution.

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