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=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