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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. 3x – 4y – 1 = 0

  2. 3x – 4y – 4 = 0

  3. 4x – 3y – 4 = 0

  4. 4x – 3y – 1 = 0


Correct Option: , 3

Solution:

x – 2y + kz = 1 ...(1)

2x + y + z = 2 ...(2)

3x – y – kz = 3 ...(3)

(1) +(3) 

$\Rightarrow 4 x-3 y=4$

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