Question

Solve the following equations:
$x-y+2z=0$
$-x+2y-z=1$
$-x+y-3z=0$

• A. $x=3,y=1andz=0$
• B. $x=1,y=0andz=0$
• C. $x=1,y=1andz=0$
• D. $x=2,y=1andz=0$

Answer 1

The correct option is C $x=1,y=1andz=0$

We have
$x-y+2z=0$...........(1)
$-x+2y-z=1$...........(2)
$-x+y-3z=0$............(3)

Adding equations (1) and (2), we get

$y+z=1$............(4)

Adding equations (1) and (3), we get

$-z=0$

$\Rightarrow z=0$.............(5)

From equations (4) and (5), we have

$y=1$

Putting $z=0andy=1$ in equation (1), we get

$x-1+0=0$

$\Rightarrow x=1$

Thus, we have

$x=1,y=1andz=0$