Question

The value of $k$ for which the system of equations $kx-y=2,6x-2y=3$ has a unique solution is _________.

• A. $=3$
• B. $\ne$ 3
• C. $\ne$ 0
• D. $=0$

Answer 1

The correct option is

A ≠ 3

For a system of equations

$a_{1}x+b_{1}y+c_1=0;a_{2}x+b_{2}y+c_2=0$

to have unique solution, the condition to be satisfied is

$\frac{a_1}{a_2}$ ≠ $\frac{b_1}{b_2}$ ≠ $\frac{c_1}{c_2}$

$\Rightarrow \frac{k}{6}$ ≠ $\frac{-1}{-2}$ ≠ $\frac{2}{3}$

$⟹\frac{k}{6}$ ≠ $\frac{1}{2}$

$⟹2k$ ≠ 6

$⟹k$ ≠ 3

$\therefore$ For unique solution of system of equations, $k$ ≠ 3