解方程组:3x+2y+2z=5 2x+3y+2z=7 2x+2y+3z=9

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解方程组:3x+2y+2z=5 2x+3y+2z=7 2x+2y+3z=9
解方程组:3x+2y+2z=5 2x+3y+2z=7 2x+2y+3z=9

解方程组:3x+2y+2z=5 2x+3y+2z=7 2x+2y+3z=9
3x+2y+2z=5 (1)
2x+3y+2z=7 (2)
2x+2y+3z=9 (3)
(1)+(2)+(3)
7x+7y+7z=21
所以x+y+z=3
所以2x+2y+2z=6 (4)
(1)-(4),x=-1
(2)-(4),y=1
(3)-(4),z=3

3x+2y+2z=5 .........(1)式
2x+3y+2z=7............(2)式
2x+2y+3z=9---------(3)式
(2)-(3)得y-z=-2.。。。。(4)式
(2)*3-(1)*2得5y+2z=11.。。。(5)式
解方程组(4)和(5)式得,z=3,y=1代入(1)式得x=-1
即:x=-1,y=1,z=3