Question

The number of solutions of the system of equations $2x+y-z=7$, $x-3y+2z=1$ and $x+4y-3z=5$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

Consider the given system of equations
$2x+y-z=7$ ....(i)
$x-3y+2z=1$ .....(ii)
and $x+4y-3z=5$ .....(iii)
From equations (i) and (ii), we get
$5x-y=15$ ....(iv)
and from equations (i) and (iii), we get
$5x-y=16$ ....(v)
Since, equations (iv) and (v) shows that they are parallel and so solution does not exist.