question_answer

The following system of linear equations

\[7x+6y-2z=0\]

\[3x+4y+2z=0\]

\[3x+4y+2z=0\]

\[x-2y-6z=0,\]   has

[JEE MAIN Held on 09-01-2020 Evening]

A) Infinitely many solutions, \[(x,y,z)\] satisfying \[x=2z\]

B) No solution

C) Only the trivial solution

D) Infinitely many solutions, \[(x,y,z)\] satisfying \[y=2z\]

Correct Answer: A

Solution :

As  \[\Rightarrow \]  The system of equations has infinite trivial solutions. Also adding equations (1) and \[3(3)\] yield \[10x=20z\Rightarrow x=2z\]