Question

For what value of $K$, the following system of equations has a unique solution.
$x-Ky=2$
$3x+2y=-5$

Answer 1

$x-Ky=2$
$3x+2y=-5$
$a_1=1$ , $b_1=-K$

$a_2=3$ , $b_2=2$
$\frac{a_1}{b_1}$ = $\frac{1}{-K}$
$\frac{a_2}{b_2}$ = $\frac{3}{2}$

$\frac{a_1}{b_1}$ $\ne$ $\frac{a_2}{b_2}$ $\to$ $\frac{1}{-K}$ $\ne$ $\frac{3}{2}$
$K$ $\ne$ $\frac{-2}{3}$

$\therefore$ $K\in R-\left(\frac{2}{3}\right)$