Solution:

Given x + 3y - z = 13....(1)

2x -5z = 23...(2)

4x - y -2z = 14 ..(3)

multiply (1) by 4

4x+12y-4z=52

and subtract (1) with (3)

13y-2z=38

again multiply (3 )by 3

we get 12x-3y-6z=42

subtract it by (1)

we get (13x-7z=55)*5

again (2x -5z = 23)*7

solving this we get x=38/17

y=40/17

z=-63/17