Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 A + C + D = 0    (1)
-1A + 2B + E = 0    (2)
-1C + E = 0    (3)
0 = 0    (4)
0 = 0    (5)
Question solving process:

Add both sides of equation (1) to both sides of equation (2) ,the equations are reduced to:
 A + C + D = 0    (1)
 2B + C + D + E = 0    (2)
-1C + E = 0    (3)
0 = 0    (4)
0 = 0    (5)

Add both sides of equation (3) to both sides of equation (2), get the equation：
 A + C + D = 0    (1)
 2B + D + 2E = 0    (2)
-1C + E = 0    (3)
0 = 0    (4)
0 = 0    (5)

Add both sides of equation (3) to both sides of equation (1), get the equation：
 A + D + E = 0    (1)
 2B + D + 2E = 0    (2)
-1C + E = 0    (3)
0 = 0    (4)
0 = 0    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A + D + E = 0    (1)
 B + 
1
2
D + E = 0    (2)
 C -1E = 0    (3)
0 = 0    (4)
0 = 0    (5)


Therefore, the solution of the equation set is:
A = -1D - 1E
B = -
1
2
D - 1E
C = 1E

Where:  D, E are arbitrary constants.
解方程组的详细方法请参阅：《多元一次方程组的解法》
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