已知3X+7Y+Z=35,4X+10Y+Z=40,求X+Y+Z的值

已知3X+7Y+Z=35,4X+10Y+Z=40,求X+Y+Z的值
已知3X+7Y+Z=35,4X+10Y+Z=40,求X+Y+Z的值

已知3X+7Y+Z=35,4X+10Y+Z=40,求X+Y+Z的值
3X+7Y+Z=35,(1)
4X+10Y+Z=40,(2)
(1)+(2),得
7X+17Y+2Z=75,(3)
(2)-(1),得
X+3Y=5,(4)
(4)*5,得
5X+15Y=25,(5)
(3)-(5),得
2X+2Y+2Z=50
所以X+Y+Z=25

X= 2
Y = 1
Z = 22
X + Y + Z = 25

1式乘以3减2式乘以2
得x+y+z=35*3-40*2=25

X=2 Y=1 z=22
答案25