Question

Find the value for k which each of the following systems of equations has a unique solution:

$x-ky=2,3x+2y+5=0.$

Answer 1

If $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$ then the pair of linear equations $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ has a unique solution.

$x-ky-2=0and3x+2y+5=0$

$a_1=1,b_1=-k,c_1=-2$

$a_2=3,b_2=2,c_2=5$

$\frac{a_1}{a_2}=\frac{1}{3}$

$\frac{b_1}{b_2}=\frac{-k}{2}$

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$


⇒$\frac{1}{3}\ne \frac{-k}{2}$

⇒$k\ne \frac{-2}{3}$