2x+y+3z=38,3x+2y+4z=56,4x+y+5z=66

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2x+y+3z=38,3x+2y+4z=56,4x+y+5z=662x+y+3z=38,3x+2y+4z=56,4x+y+5z=662x+y+3z=38,3x+2y+4z=56,4x+y+5z=66（

2x+y+3z=38,3x+2y+4z=56,4x+y+5z=66
2x+y+3z=38,3x+2y+4z=56,4x+y+5z=66

2x+y+3z=38,3x+2y+4z=56,4x+y+5z=66
（1）2x+y+3z=38
（2）3x+2y+4z=56
（3）4x+y+5z=66
（1）（3）式相减得（4）
2x+2z=28
（4）x+z=14
（3）两边同时×2得（5）
8x+2y+10z=132与（2）相减得（5）
3x+2y+4z=56
（5）5x+6z=76
由（4）得
x=14-z代入到（5）
5（14-z）+6z=76
70-5z+6z=76
z=6
x=14-6=8
把x、z代入到（1）
16+y+18=38
y=4
所以
x=8
y=4
z=6

1式乘2减3式：y+z=10;
2式减1式：x+y+z=18;
x=8,代入1式：y+3z=22;
z=6,y=4.

x=8,y=4,z=6
令2x+y+3z=38为a式,3x+2y+4z=56为b式,4x+y+5z=66 为c式
则c减b为x-y+z=10,c-a得x+z=14,y=4
2倍的a减去c得4x-4x+2y-y+6z-5z=10即y+z=10,z=6,
将x,y值代入a,得x=8

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