若x,y,z,满足3x+2y+z=5,2x+y-3z=1.y是非负数.求z的取值范围
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若x,y,z,满足3x+2y+z=5,2x+y-3z=1.y是非负数.求z的取值范围若x,y,z,满足3x+2y+z=5,2x+y-3z=1.y是非负数.求z的取值范围若x,y,z,满足3x+2y+z
若x,y,z,满足3x+2y+z=5,2x+y-3z=1.y是非负数.求z的取值范围
若x,y,z,满足3x+2y+z=5,2x+y-3z=1.y是非负数.求z的取值范围
若x,y,z,满足3x+2y+z=5,2x+y-3z=1.y是非负数.求z的取值范围
解前两个方程把X消掉 求出Y=7-11Z
因为Y≥0
所以7-11ZY≥0
所以Z≤7/11
3x+2y+z=5,(1)
2x+y-3z=1,(2)
(1)*2得
6x+4y+2z=5,(3)
(2)*3得
6x+3y-9z=3,(4)
(3)-(4)得
y=2-11z,
因为y是非负数,
所以2-11z≥0,
所以-11z≥-2,
所以z≤2/11.
方法:2个式子削去X,然后Y=(用Z表示的数字),Y是小于0,可以得到Z的范围
3x+2y+z=5
2x+y-3z=1
y>=0
得:
6x+4y+2z=10
6x+3y-9z=3
两试相减
y-7z=7
得
y=7z+7
代入y>=0得
7z+7>=0
则z>=1
3x+2y+z=5 A
2x+y-3z=1 B 则2A-3B得:y+11z=7,因为y大于等于0,所以z小于等于11/7
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