（急!）解三元一次的题,①x+y+z=1 x+3y+7z=2 x+5y+19z=4②x+2y+3z=1 x=y+1 2x

①x+y+z=1 x+3y+7z=2 x+5y+19z=4
x+3y+7z-(x+y+z)=2-1 得2y+6z=1
x+5y+19z-(x+3y+7z)=4-2 得2y+12z=2
可知z=1/6,y=0,代入x+y+z=1,得x=5/6
②x+2y+3z=1 x=y+1 2x+3y+5z=2
将x=y+1代入x+2y+3z=1得y=-z
将x=y+1代入2x+3y+5z=2得y=-z,
所以假设y=a,则x=a+1,z=-a,有无穷多个解.
③x+y+z=1 x-y-z-3=0 x+2y+3z=-4
x+y+z+(x-y-z-3)=1得x=2
x+2y+3z-2(x+y+z)=-4-2得x-z=6,所以z=-4
代入x+y+z=1,y=3
④3x+4z=23 5x+y=8 6x+y+8z=49
6x+y+8z-2(3x+4z)=49-23*2得y=3
代入5x+y=8,得x=1
代入3x+4z=23,得z=5

x+3y+7z-(x+y+z)=1,y+3z=0.5;
x+5y+19z-(x+y+z)=3,y+9/2z=0.75;
y+9/2z-(y+3z)=0.25,z=1/6;
y+3z=y+0.5=0.5,y=0;
x+y+z=x+0+1/6=1,x=5/6;
x=5/6,y=0,z=1/6;
同法解即可。

x+3y+7z-(x+y+z)=1,y+3z=0.5;
x+5y+19z-(x+y+z)=3,y+9/2z=0.75;
y+9/2z-(y+3z)=0.25,z=1/6;
y+3z=y+0.5=0.5,y=0;
x+y+z=x+0+1/6=1,x=5/6;
x=5/6,y=0,z=1/6;