求解三元一次方程：x+y-5z=16,y+z-5x=4,z+x-5y=-14

题目

求解三元一次方程：x+y-5z=16,y+z-5x=4,z+x-5y=-14

答案

x+y-5z=16 (1)
y+z-5x=4 (2)
z+x-5y=-14 (3)
(1)+(2)+(3)
-3(x+y+z)=6
x+y+z=-2 (4)
(4)-(2)
6x=-6 x=-1
(4)-(3)
6y=12 y=2
(4)-(1)
6z=-18 z=-3
x=-1 y=2 z=-3