Question

Find the value (s) of k for which the pair of equations $\left\{\begin{array}{l}\boldsymbol{k x}+2 \boldsymbol{y}=\mathbf{3} \\ \mathbf{3 x}+6 \boldsymbol{y}=\mathbf{1 0}\end{array}\right.$ has a unique solution.

Answer 1

Given : pair of equation is $k x+2 y=3$

$3 x+6 y=10$

For a unique solution, $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$

Here, $a_1=k, b_1=2$

$a_2=3, b=6$

$\begin{aligned}\frac{k}{3} & \neq \frac{2}{6} \\k & \neq 1\end{aligned}$

Hence, the pair of equation has a unique solution for all real values of $k$ except 1.