If the system of linear equations x−2y+kz=1 2x+y+z=2, 3x−y−kz=3has a solution (x,y,z), z≠0,Then (x, y)lies on the straight line whose equation is

x−2y+kz=1→(1)2x+y+z=2→(2)3x−y−kz=3→(3)(1)+(3)⇒4x−3y=4⇒(x, y)lies on the straight line 4x−3y−4=0

If the system of linear equations x−2y+kz=1 2x+y+z=2, 3x−y−kz=3has a solution (x,y,z), z≠0,Then (x, y)lies on the straight line whose equation is

x−2y+kz=1→(1)2x+y+z=2→(2)3x−y−kz=3→(3)(1)+(3)⇒4x−3y=4⇒(x, y)lies on the straight line 4x−3y−4=0

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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

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$3 x - 4 y - 1 = 0$

$3 x - 4 y - 4 = 0$

$4 x - 3 y - 4 = 0$

$4 x - 3 y - 1 = 0$

answer is C.

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Detailed Solution

$x - 2 y + k z = 1 \to (1)$

$2 x + y + z = 2 \to (2)$

$3 x - y - k z = 3 \to (3)$

$(1) + (3) \Rightarrow 4 x - 3 y = 4 \Rightarrow (x, y)$

lies on the straight line $4 x - 3 y - 4 = 0$

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If the system of linear equations x−2y+kz=1 2x+y+z=2, 3x−y−kz=3has a solution (x,y,z), z≠0,Then (x, y)lies on the straight line whose equation is

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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