−x + 2y − z = 0
−x − y + 2z = 0
2x − z = 8

Step-by-step explanation:

several possibilities to solve this.

let's start with subtracting the second equation from the first

-x + 2y - z = 0

- -x - y +2z = 0

0 3y - 3z = 0

y - z = 0

y = z

now we use this in e.g. the first equation :

-x + 2z - z = 0

-x + z = 0

z = x (therefore, also x = y)

now we use this in the third equation :

2x - x = 8

x = 8 = y = z

the correct answer is c