hello :
2x+3y+z=17 ...(1)
x-3y+2z=-8 ...(2)
5x-2y+3z=5 ...(3)
by(2) : x =3y -2x - 8
subsct : x in (1) and (2) :
2 (3y -2z - 8) +3y +z = 17
5(3y -2z - 8)- 2y+3z = 5
I'have a system :
9y - 3z = 33 ..(*)
13y - 7z = 45 (**)
divided (-) by : 3
3y - z = 11
z= 3y -11
subsct in (**) : 13y - 7(3y -11) =45
- 8y= -32
y =4
but : z= 3y -11
so : z = 3(4)-11 = 1
but : x =3y -2x - 8
so : x = 3(4)-2(1)-8 =2
coclusion : one solution : (2 , 4 , 1 )