2x+3y+z=17

x-3y+2x=-8

5x-2y+3z=5

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)