For what values of k does the pair of equations x−2y=33

SOLUTION

Concept : 1 Mark
Application : 1 Mark

Given equations are,

$x-2y=3\Rightarrow x-2y-3=0\dots \dots \left(i\right)$

$a_1=1,b_1=-2,c_1=3$

$3x+ky=1\Rightarrow 3x+ky-1=0\dots \dots \left(ii\right)$

$a_2=3,b_2=k,c_2=-1$

For pair of equations to have unique solution,

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

$\frac{1}{3}\ne \frac{-2}{k}$

$\Rightarrow k\ne -6$