2x+y+z=18 4x+2y-z=17 3x-y+2z=19

2x +y+z = 18...2×
4x+2y-z = 17...1×

4x+2y+2z = 36
4x+2y-z = 17
———————— (-)
3z = 19
z = 19/3 = 6⅓

2x+y+z = 18
3x-y+2z= 19
———————(+)
5x+3z = 37

5x+3z = 37
5x+3(19/3) = 37
5x = 37 -28/3 = 111/3 -28/3 = 83/3 =27⅔
x = 27⅔ : 5 = 83/3 × 3/15 = 249/45 =5 24/45 = 5 8/15
x = 5 8/15

2x+y+z = 18
2(83/15)+y+(19/3) = 18
y = 18 -113/15 -19/3
y = 270/15 -113/15 -95/15
y = 62/15
y = 4 2/15

HP = {5 8/15 ,4 2/15 & 6⅓}