若X+2Y+3Z=10,4X+3Y+2Z=15.则X+Y+Z=?

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若X+2Y+3Z=10,4X+3Y+2Z=15.则X+Y+Z=?

若X+2Y+3Z=10,4X+3Y+2Z=15.则X+Y+Z=?
若X+2Y+3Z=10,4X+3Y+2Z=15.则X+Y+Z=?

若X+2Y+3Z=10,4X+3Y+2Z=15.则X+Y+Z=?
2等式一加,左边加左边,右边加右边
得5(x+y+z)=25
x+y+z=5

(x+2y+3z)+(4x+3y+2z)=25
5x+5y+5z=25
x+y+z=5

X+Y+Z=5
X+2Y+3Z=10
+ 4X+3Y+2Z=15
= 5X+5Y+5Z=25
所以,X+Y+Z=5

令A=x+y+z;
x+2y+3z = A+y+2z = 10 (1)
4x+3y+2z = 2A+2x+y = 15 (2)
两式相加:3A+2x+2y+2z = 5A =25
所以A=5