If the system of linear equations
Question:

If the system of linear equations

$x-2 y+k z=1$

$2 x+y+z=2$

$3 x-y-k z=3$

has a solution $(x, y, z), z \neq 0$, then $(x, y)$ lies on the straight line whose equation is :

1. $3 x-4 y-1=0$

2. $3 x-4 y-4=0$

3. $4 x-3 y-4=0$

4. $4 x-3 y-1=0$

Correct Option: , 3

Solution:

$x-2 y+k z=1$ …………(1)

$2 x+y+z=2$ …………..(2)

$3 x-y-k z=3$ ………….(3)

(1) $+(3)$

$\Rightarrow 4 x-3 y=4$