3x-y+z=3,2x+3y-z=12,x+y+z=6解方程组
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3x-y+z=3,2x+3y-z=12,x+y+z=6解方程组3x-y+z=3,2x+3y-z=12,x+y+z=6解方程组3x-y+z=3,2x+3y-z=12,x+y+z=6解方程组3x-y+z=
3x-y+z=3,2x+3y-z=12,x+y+z=6解方程组
3x-y+z=3,2x+3y-z=12,x+y+z=6
解方程组
3x-y+z=3,2x+3y-z=12,x+y+z=6解方程组
3x-y+z=3 (1)
2x+3y-z=12 (2)
x+y+z=6 (3)
(1)+(2)得:
5x+2y=15
再乘以2得:
10x+4y=30 (4)
(2)+(3)得:
3x+4y=18 (5)
(4)-(5)得:
7x=12
x=12/7;
代入(5)得:y=(18-3x)/4=45/14;
z=6-x-y=6- 12/7 - 45/14=15/14;
所以解集为:
x=12/7;
y=45/14;
z=15/14;
设为①②③式
①+②=5x+2y=15设为④
②+③=3x+4y=18设为⑤
2④-⑤=7x=12所以x=12/7
y=45/14
Z=15/14
3x-y+z=3 (1)
2x+3y-z=12 (2)
x+y+z=6 (3)
(1)+(2)
5x-2y=15 (4)
(2)+(3)
3x+4y=18 (5)
(4)×2+(5)
10x+3x=30+18
13x=48
所以
x=48/13
y=(5x-15)/2=45/26
z=6-x-y=15/26
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