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