x+3y+2z=17....①
2y-x+3z=8....②
x+y+z=10....③
①-③得
2y+z=7....④
②+③得
3y+4z=18....⑤
4④-⑤得
5y=10
y=2
y=2带入④得
z=3
y=2,z=3带入③得
x=5
所以x=5,y=2,z=3
x+3y+2z=17 (1)
-x+2y+3z=8 (2)
x+y+z=10 (3)
(1)+(2)
5y+5z=25
y+z=5 (4)
(2)+(3)
3y+4z=18 (5)
(5)-3(4)
z=3
from (4)
y+z=5
y+3=5
y=2
from (1)
x+3y+2z=17
x+6+6=17
x=5
(x,y,z)=(5,2,3)
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