Question

The pair of linear equations $2x+ky-3=0,6x+\frac{2}{3}y+7=0$ has a unique solution if

• A. $k=\frac{2}{3}$
• B. $k\ne \frac{2}{3}$
• C. $k=\frac{2}{9}$
• D. $k\ne \frac{2}{9}$

Answer 1

The correct option is D $k\ne \frac{2}{9}$

The equation are
$\Rightarrow 2x+ky-3=0$
$\Rightarrow 6x+\frac{2}{3}y+7=0$
$\Rightarrow a_1=2,b_1=k,c_1=-3$
$\Rightarrow a_2=6,b_2=\frac{2}{3},c_2=7$
$Forthesystemtohaveuniquesolution$
$\Rightarrow \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
$\Rightarrow \frac{2}{6}\ne \frac{k}{\frac{2}{3}}$
$\Rightarrow k\ne \frac{2}{9}$