2x+y+z=15 x+2y+z=16 x+y+2z=17

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2x+y+z=15 x+2y+z=16 x+y+2z=17
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2x+y+z=15 x+2y+z=16 x+y+2z=17
2x+y+z=15 x+2y+z=16 x+y+2z=17

2x+y+z=15 x+2y+z=16 x+y+2z=17
2x+y+z=15 (1)
x+2y+z=16 (2)
(1)-2(2)
3y+z=17
x+y+2z=17 (3)
(2)-(3)
y-z=-1
4y=16
y=4
z=5
x=3

x+y+z=15-x x+y+x=16-y x+y+x=17-z
15-x=16-y y=x+1
15-x=17-z z=x+2
x+x+1+x+2=15-x
4x=12
x=3
y=4
z=5