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

2x-y+2z=8......(2)

x+y+z= 3......(3)

First we will add(3) and (2):

==> 3x +3z = 11........(4)

Now multiply (2) by 2 and then add to (1):

==> 5x +3z = 19.....(5)

Now subtract (4) from (5):

==> 2x = 8

==> **x= 4**

Substitute in (5) :

5(4) + 3z = 19

==> 3z= -1

==> **z= -1/3**

Now substitute in (3):

4+ y -1/3 = 3

==> y= -1+1/3

==> **y= -2/3**