Question

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

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

Answer 1

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

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

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

$3x+2y=2$............(4)

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

$2x+2y=2$............(5)

Subtracting equation (5) from (4), we get

$x=0$

Putting $x=0$ in equation 5, we get

$0+2y=2$

$\Rightarrow y=1$

Putting $y=1andx=0$ in equation (1), we get

$0+1+2z=1$

$\Rightarrow z=0$

Thus, we have

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