x-2y=9 x+y+z=7 2x-3y=12
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x-2y=9 x+y+z=7 2x-3y=12
不妨方程x-2y=-9标注为(1),方程3x-y+z=4标注为(2),方程y-z=3标注为(3),则有
(2)-(1)*3=(3x-y+z)-(x-2y)*3=4-(-9)x3,
即为5y+z=31,标注为(4)
(3)+(4)=(y-z)+(5y+z)=3+31,
即6y=34,可得y=17/3
将y=17/3代入(1),
则有x-2*17/3=-9,可得x=7/3
将y=17/3代入(3),
则有17/3-z=3,可得z=8/3
综上:x=7/3,y=17/3,z=8/3
不妨方程2x+3y-z=12 标注为(1),方程2z+x=47标注为(2),方程x+y+z=6标注为(3),则有
(3)*3-(1)=(x+y+z)*3-(2x+3y-z)=6*3-12,
即为x+4z=6,标注为(4)
则(4)-(3)=(x+4z)-(2z+x)=6-47,
即为2z=-41,则z=-20.5
将z=-20.5代入(4),可得x=6-4*(-20.5)=88
再将x=88,z=-20.5代入(3)得
y=6-88-(-20.5)=-61.5
综上可得:x=88,y=-61.5,z=-20.5
(2)-(1)*3=(3x-y+z)-(x-2y)*3=4-(-9)x3,
即为5y+z=31,标注为(4)
(3)+(4)=(y-z)+(5y+z)=3+31,
即6y=34,可得y=17/3
将y=17/3代入(1),
则有x-2*17/3=-9,可得x=7/3
将y=17/3代入(3),
则有17/3-z=3,可得z=8/3
综上:x=7/3,y=17/3,z=8/3
不妨方程2x+3y-z=12 标注为(1),方程2z+x=47标注为(2),方程x+y+z=6标注为(3),则有
(3)*3-(1)=(x+y+z)*3-(2x+3y-z)=6*3-12,
即为x+4z=6,标注为(4)
则(4)-(3)=(x+4z)-(2z+x)=6-47,
即为2z=-41,则z=-20.5
将z=-20.5代入(4),可得x=6-4*(-20.5)=88
再将x=88,z=-20.5代入(3)得
y=6-88-(-20.5)=-61.5
综上可得:x=88,y=-61.5,z=-20.5
x-2y=9 x+y+z=7 2x-3y=12
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