帮忙解四元一次方程w+x+y+z=02w+3x=84y+7z=95x+y=4求wxy*z（精确到十位）

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帮忙解四元一次方程
w+x+y+z=0
2w+3x=8
4y+7z=9
5x+y=4
求w*x*y*z（精确到十位）

w + x + y + z = 0
2w + 3x = 8
4y + 7z = 9
5x + y = 4
10x + 2y = 8 = 2w + 3x
2w + 3x = 10x + 2y
2w - 7x - 2y = 0
2w + 2x + 2y + 2z = 0
4w - 5x + 2z = 0
5x = 4w + 2z
5x + y = 4
5x = 4 - y = 4w + 2z
4w + 2z = 4 - y
y = 4 - 4w - 2z
这样
w + x + z + 4 - 4w - 2z = 0
4 - 3w + x - z = 0
3w - x + z = 4
4( 4 - 4w - 2z ) + 7z = 9
16 - 16w - 8z + 7z = 9
7 - 16w - z = 0
16w + z = 7
3w - x + z + 7 - 16w - z = 4
3 - 13w - x = 0
13w + x = 3
39w + 3x = 9
2w + 3x = 8
37w = 1
w = 1/37
13w + x = 3
x = 3 - 13/37
16w + z = 7
z = 7 - 16/37
5x + y = 4
y = 4 - 5X ( 3 - 13/37 )
= 4 - 15 + 65/37
= -11 + 2 - 9/37
= -9 - 9/37
w*y
= ( 1/37 ) X ( -9 - 9/37 )
= ( -9/37 )( 1 + 1/37 )
= ( -9 )( 38/1369 )
= -342 /1369
x*z
= ( 3 - 13/37 ) X ( 7 - 16/37 )
= 21 + 208/1369 - 48/37 - 91/37
= 21 + 208/1369 - 1 - 11/37 - 3 + 20/37
= 17 + 208/1369 - 407/1369 + 740/1369
= 17 + 948/1369 - 407/1369
= 17 + 541/1369
w*x*y*z
= ( - 342 /1369 ) X ( 17 + 541/1369 )
= - 17 X 342/1369 - 342/1369 X 541/1369
= - 5814/1369 - ( 342X541 / 1369X1369 )
= - 4 - 338/1369 - ( 342X541 / 1369X1369 )
w*x*y*z 近似值就是 -4

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