If system of linear equations x - 2y + kz = 1 ; 2x + y + z = 2 ; 3x - y - kz = 3 &

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3 and 4 .Determinants and Matrices

hard

If the system of linear equations $x - 2y + kz = 1$ ; $2x + y + z = 2$ ; $3x - y - kz = 3$ Has a solution $(x, y, z) \ne 0$, then $(x, y)$ lies on the straight line whose equation is

A

$3x -4y -1 = 0$

B

$4x -3y -4 = 0$

C

$4x -3y -1 = 0$

D

$3x -4y -4 = 0$

(JEE MAIN-2019)

Solution

For infinitly many solution

$\left| {\begin{array}{*{20}{c}}
1&{ – 2}&k\\
2&1&1\\
3&{ – 1}&{ – k}
\end{array}} \right| – 0$

$ \Rightarrow k = \frac{{ – 1}}{2}$

Also consider

$x – 2y + k = 1$ and $2x + y + z = 2$

$ \Rightarrow 2x – 4y – z – 2$

$2x + y + z = 2$

$ \Rightarrow 4x – 3y = 4$

Standard 12

Mathematics

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