用加减消元法解方程组x+y=10 y+z=22 z+x=18

x+y=10 (1)
y+z=22 (2)
z+x=18 (3)
(1)+(2)+(3)
x+y+y+z+z+x=10+22+18
2(x+y+z)=50
x+y+z=25 (4)
(4)-(1) z=15
(4)-(2) x=3
(4)-(3) y=7

x+y=10 ①
y+z=22 ②
z+x=18 ③
③-①得：z-y=8
z=y+8 代入②：
y+y+8=22
2y=14
y=7
x=10-7=3
z=22-7=15

依次1,2,3式
1-2: x-z=-12---4
2-3: y-x=4-----5
5+1: y=7
4+3: x=3
z=15