Find the value of $K$ for which equation $x-Ky=2$, $3x+2y=5$ has unique solution.

1. A system of linear equations $a_{1}x+b_{1}y=c_1$ and $a_{2}x+b_{2}y=c_2$ has a unique solution if:
$$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$$
Identify the coefficients from the given equations:Equation 1: $1x-Ky=2⟹a_1=1,b_1=-K$ Equation 2: $3x+2y=5⟹a_2=3,b_2=2$ Substitute these coefficients into the condition for uniqueness:
$$\frac{1}{3}\ne \frac{-K}{2}$$
Cross-multiply to solve for $K$:
$$2\ne -3K⟹K\ne -\frac{2}{3}$$