Question 331405
three equations and three unknows x,y,z

1)   x+y+z=1         
2)   x-y+3z=17         Lets take equation 1 and 2 then eliminate y by adding 
3)   2x+y+z=-2             1)  x+y+z=1
                            2) x-y+3z=17    adding we get equation 4) 2x+4z=18
                       next take eq 2 and 3 and eliminate the same variable y
                        2) x-y+3z=17
                        3) 2x+y+z=-2         adding we get eq 5)3x+4z=15
2x+4z=18  and 3x+4z=15 multiply eq 4) by -1 and add

-2x-4z=-18
 3x+4z=15        adding we get -2x+3x-4z+4z=-18+15......x=-3 plug -3 in eq 4
2*-3+4z=18...-6+4z=18 solve for z by adding 6 then divide by 4

4z=24.........z=6      finialy use x=-3 asnd z=6 and plug into eq 1)

-3+y+6=1......y+3=1........y=-2  so we get (-3,-2,6)  plug these into eq 1)
-3-2+6=1 to check 1=1 your solution is (-3,-2,6)   

I hope this is not to crowed, good luck!