4x+2y+5z=1 x-2y-2z=2 3x+2y-z=5三元一次方程

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4x+2y+5z=1 x-2y-2z=2 3x+2y-z=5三元一次方程
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4x+2y+5z=1 x-2y-2z=2 3x+2y-z=5三元一次方程
4x+2y+5z=1 x-2y-2z=2 3x+2y-z=5
三元一次方程

4x+2y+5z=1 x-2y-2z=2 3x+2y-z=5三元一次方程
4x + 2y + 5z = 1 (1)
x - 2y - 2z = 2 (2)
3x + 2y -z = 5 (3)
(1) + (2)得:5x + 3z = 3 (4)
(2) + (3)得:4x - 3z = 7 (5)
( 4) + (5)得:9x = 10 解得:x = 10/9
将 x = 10/9代入(4)得 3z = 3 - 5x 则z = (3 - 5x)/3 = (3 - 5×10/9)/3 = -23/27
把x = 10/9 z = -23/27代入(1)得:2y = 1 - 4x - 5z
y = (1 -4x - 5z)/2
= (1 - 4× 10/9 - 5×(-23/27) )/2
= 11/27
所以,原方程组的解是 x = 10/9 y = 11/27 z = -23/27