Question

Let $k$ be a constant. The equations $kx + y = 3$ and $4x + ky = 4$ have a unique solution if and only if

• A. $|k|≠2$
• B. $|k|=2$
• C. $k≠2$
• D. $k=2$

Answer 1

Answer: (A)

$|k|≠2$

Answer 2

Simultaneous equation have a unique solution only if $\frac{a_1}{a_2}≠\frac{b_1}{b_2}$
From the given equations, a unique solution would exist only if $\frac{k}{2}≠\frac{2}{k}$
$⇒ k^2≠4⇒|k|≠2$
So, the correct option is (A): $|k|≠2$