SOLUTION: Solving systemn of equations in three variables x-y-Z=0 2x-3y+2z=7 -x+2y+z=1 thank you

 x -  y -  z = 0,    (1)
2x - 3y + 2z = 7,    (2)
-x + 2y +  z = 1.    (3)

Add equations (1) and (3). You will get 

0x +  y + 0z = 1,    or simply   y = 1.

So, you just found one unknown: y = 1.

Now substitute this value of y into equations (1) and (2):

 x -   1 -  z = 0,   (4)
2x - 3*1 + 2z = 7.   (5)

Simplify it and write it in canonical form:

  x -  z =  1,       (4')
2x  + 2z = 10.       (5')

Divide (5') by 2 (both sides).

You will get the system (4'),(5') in the form

  x -  z =  1,       (4'')
  x  + z =  5.       (5'')

Now, add equations (4'') and (5''). You will get

  2x = 6   --->  x = 3.

I leave it to you to find the last remaining unknown z.