若3x+7y+z=315,4x+10y+z=420,则x+y+z=________________.

题目

若3x+7y+z=315,4x+10y+z=420,则x+y+z=________________.

答案

3X+7Y+Z=315 (1)
4X+10Y+Z=420 (2)
(2)-(1):X+3Y=105,所以:X=105-3Y.(3)
把(3)代入(1)中:
3(105-3Y)+7Y+Z=315,化简:-2Y+Z=0,则:
X+Y+Z=105-3Y+Y+Z=105-2Y+Z=105