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On line solution of multivariate equations：
    First set the elements of the equation (i.e. the number of unknowns), then click the "Next" button to enter the coefficients of each element of the equation set, and click the "Next" button to obtain the solution of the equation set.
    Note that the coefficients of each element of the equation system can only be numbers, not algebraic expressions (including mathematical functions).
    Current location：Equations > Multivariate equations > Answer
detailed information：
The input equation set is:
 2A + 12B + 8D = 40    (1)
-10A + 10B + 4C = -20    (2)
-4C + 8D + 8E = 20    (3)
 B -1C -1D = 0    (4)
-1A -1B + D -1E = 0    (5)
Question solving process:

Multiply both sides of equation (1) by 5, the equation can be obtained:
         10A + 60B + 40D = 200    (6)
, then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
 B -1C -1D = 0    (4)
-1A -1B + D -1E = 0    (5)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         A + 6B + 4D = 20    (7)
, then add the two sides of equation (7) to both sides of equation (5), the equations are reduced to:
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
 B -1C -1D = 0    (4)
 5B + 5D -1E = 20    (5)

Divide the two sides of equation (2) by 70, the equation can be obtained:
         B + 
2
35
C + 
4
7
D = 
18
7
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
- 
37
35
C - 
11
7
D = - 
18
7
    (4)
 5B + 5D -1E = 20    (5)

Divide the two sides of equation (2) by 14, the equation can be obtained:
         5B + 
2
7
C + 
20
7
D = 
90
7
    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
- 
37
35
C - 
11
7
D = - 
18
7
    (4)
- 
2
7
C + 
15
7
D -1E = 
50
7
    (5)

Multiply both sides of equation (3) by 37
Divide the two sides of equation (3) by 140, the equation can be obtained:
        - 
37
35
C + 
74
35
D + 
74
35
E = 
37
7
    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
- 
129
35
D - 
74
35
E = - 
55
7
    (4)
- 
2
7
C + 
15
7
D -1E = 
50
7
    (5)

Divide the two sides of equation (3) by 14, the equation can be obtained:
        - 
2
7
C + 
4
7
D + 
4
7
E = 
10
7
    (11)
, then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
- 
129
35
D - 
74
35
E = - 
55
7
    (4)
 
11
7
D - 
11
7
E = 
40
7
    (5)

Multiply both sides of equation (4) by 55
Divide the two sides of equation (4) by 129, the equation can be obtained:
        - 
11
7
D - 
814
903
E = - 
3025
903
    (12)
, then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
- 
129
35
D - 
74
35
E = - 
55
7
    (4)
- 
319
129
E = 
305
129
    (5)

Multiply both sides of equation (5) by 9546
Divide both sides of equation (5) by 11165, get the equation：
        - 
74
35
E = 
4514
2233
    (13)
, then subtract both sides of equation (13) from both sides of equation (4), get the equation：
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D + 8E = 20    (3)
- 
129
35
D = - 
22059
2233
    (4)
- 
319
129
E = 
305
129
    (5)

Multiply both sides of equation (5) by 1032
Divide both sides of equation (5) by 319, get the equation：
        -8E = 
2440
319
    (14)
, then add the two sides of equation (14) to both sides of equation (3), get the equation：
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C + 8D = 
8820
319
    (3)
- 
129
35
D = - 
22059
2233
    (4)
- 
319
129
E = 
305
129
    (5)

Multiply both sides of equation (4) by 280
Divide both sides of equation (4) by 129, get the equation：
        -8D = - 
6840
319
    (15)
, then add the two sides of equation (15) to both sides of equation (3), get the equation：
 2A + 12B + 8D = 40    (1)
 70B + 4C + 40D = 180    (2)
-4C = 
180
29
    (3)
- 
129
35
D = - 
22059
2233
    (4)
 E = - 
305
319
    (5)

Multiply both sides of equation (4) by 1400
Divide both sides of equation (4) by 129, get the equation：
        -40D = - 
34200
319
    (16)
, then add the two sides of equation (16) to both sides of equation (2), get the equation：
 2A + 12B + 8D = 40    (1)
 70B + 4C = 
23220
319
    (2)
-4C = 
180
29
    (3)
- 
129
35
D = - 
22059
2233
    (4)
 E = - 
305
319
    (5)

Multiply both sides of equation (4) by 280
Divide both sides of equation (4) by 129, get the equation：
        -8D = - 
6840
319
    (17)
, then add the two sides of equation (17) to both sides of equation (1), get the equation：
 2A + 12B = 
5920
319
    (1)
 70B + 4C = 
23220
319
    (2)
-4C = 
180
29
    (3)
- 
129
35
D = - 
22059
2233
    (4)
 E = - 
305
319
    (5)

Add both sides of equation (3) to both sides of equation (2), get the equation：
 2A + 12B = 
5920
319
    (1)
 70B = 
25200
319
    (2)
-4C = 
180
29
    (3)
 D = 
855
319
    (4)
 E = - 
305
319
    (5)

Multiply both sides of equation (2) by 6
Divide both sides of equation (2) by 35, get the equation：
         12B = 
4320
319
    (18)
, then subtract both sides of equation (18) from both sides of equation (1), get the equation：
 2A = 
1600
319
    (1)
 70B = 
25200
319
    (2)
 C = - 
45
29
    (3)
 D = 
855
319
    (4)
 E = - 
305
319
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
800
319
    (1)
 B = 
360
319
    (2)
 C = - 
45
29
    (3)
 D = 
855
319
    (4)
 E = - 
305
319
    (5)


Therefore, the solution of the equation set is:
A = 
800
319
B = 
360
319
C = - 
45
29
D = 
855
319
E = - 
305
319


Convert the solution of the equation set to decimals:
A = 2.507837
B = 1.128527
C = -1.551724
D = 2.680251
E = -0.956113

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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