x1-x2+x3=1 (1)
x2-x3+x4=2 (2)
x3-x4+x5=3 (3)
x4-x5+x1=4 (4)
x5-x1+x2=5 (5)
(1)+(2)+(3)+(4)+(5)
x1+x2+x3+x4+x5=15 (6)
(1)+(2) x1+x4=3 (7)
(2)+(3) x2+x5=5 (8)
(3)+(4) x1+x3=7 (9)
(4)+(5) x2+x4=9 (10)
(5)+(1) x3+x5=6 (11)
(7)、(8)代入(6)
x3+3+5=15 x3=7
x3=7代入(9) x1=7-x3=7-7=0
x1=0代入(7) x4=3-x1=3-0=3
x3=7代入(11) x5=6-x3=6-7=-1
x=5代入(8) x2=5-x5=5-(-1)=6
x=2代入(10) x4=9-x2=9-6=3
综上,得x1=0 x2=6 x3=7 x4=3 x5=-1