CAT 2020 Slot 3 QA Question 4: Let $k$ be a constant. The equations $kx + y = 3$ and $4x + ky = 4$ have a unique solution if and only if

Question

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

Accepted Answer

A pair of linear equations has a unique solution when the determinant of the coefficient matrix is non-zero.
Coefficient determinant = $k 	imes k - 4 	imes 1 = k^2 - 4$
$\Rightarrow k^2 - 4 
e 0$
$\Rightarrow k^2 
e 4$
$\Rightarrow |k| 
e 2$
Therefore, the equations have a unique solution if an

Let kkk be a constant. The equations kx+y=3kx + y = 3kx+y=3 and 4x+ky=44x + ky = 44x+ky=4 have a unique solution if and only if

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