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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:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
 
27
20
A + 
13
10
B + 
13
10
C + 
13
10
D + 
13
10
E = 455    (2)
 
13
10
A + 
13
10
B + 2C + 
13
10
D + 
13
10
E = 380    (3)
 
13
10
A + 
13
10
B + 
13
10
C + D + 
13
10
E = 300    (4)
 
13
10
A + 
13
10
B + 
13
10
C + 
13
10
D + E = 227    (5)
Question solving process:

Multiply both sides of equation (1) by 27
Divide the two sides of equation (1) by 28, the equation can be obtained:
         
27
20
A + 
729
560
B + 
729
560
C + 
729
560
D + 
729
560
E = 
7155
14
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D - 
1
560
E = - 
785
14
    (2)
 
13
10
A + 
13
10
B + 2C + 
13
10
D + 
13
10
E = 380    (3)
 
13
10
A + 
13
10
B + 
13
10
C + D + 
13
10
E = 300    (4)
 
13
10
A + 
13
10
B + 
13
10
C + 
13
10
D + E = 227    (5)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 14, the equation can be obtained:
         
13
10
A + 
351
280
B + 
351
280
C + 
351
280
D + 
351
280
E = 
3445
7
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D - 
1
560
E = - 
785
14
    (2)
 
13
280
B + 
209
280
C + 
13
280
D + 
13
280
E = - 
785
7
    (3)
 
13
10
A + 
13
10
B + 
13
10
C + D + 
13
10
E = 300    (4)
 
13
10
A + 
13
10
B + 
13
10
C + 
13
10
D + E = 227    (5)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 14, the equation can be obtained:
         
13
10
A + 
351
280
B + 
351
280
C + 
351
280
D + 
351
280
E = 
3445
7
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D - 
1
560
E = - 
785
14
    (2)
 
13
280
B + 
209
280
C + 
13
280
D + 
13
280
E = - 
785
7
    (3)
 
13
280
B + 
13
280
C - 
71
280
D + 
13
280
E = - 
1345
7
    (4)
 
13
10
A + 
13
10
B + 
13
10
C + 
13
10
D + E = 227    (5)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 14, the equation can be obtained:
         
13
10
A + 
351
280
B + 
351
280
C + 
351
280
D + 
351
280
E = 
3445
7
    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D - 
1
560
E = - 
785
14
    (2)
 
13
280
B + 
209
280
C + 
13
280
D + 
13
280
E = - 
785
7
    (3)
 
13
280
B + 
13
280
C - 
71
280
D + 
13
280
E = - 
1345
7
    (4)
 
13
280
B + 
13
280
C + 
13
280
D - 
71
280
E = - 
1856
7
    (5)

Multiply both sides of equation (2) by 26, the equation can be obtained:
        - 
13
280
B - 
13
280
C - 
13
280
D - 
13
280
E = - 
10205
7
    (10)
, then add the two sides of equation (10) to both sides of equation (3), the equations are reduced to:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D - 
1
560
E = - 
785
14
    (2)
 
7
10
C = -1570    (3)
 
13
280
B + 
13
280
C - 
71
280
D + 
13
280
E = - 
1345
7
    (4)
 
13
280
B + 
13
280
C + 
13
280
D - 
71
280
E = - 
1856
7
    (5)

Multiply both sides of equation (2) by 26, the equation can be obtained:
        - 
13
280
B - 
13
280
C - 
13
280
D - 
13
280
E = - 
10205
7
    (11)
, then add the two sides of equation (11) to both sides of equation (4), the equations are reduced to:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D - 
1
560
E = - 
785
14
    (2)
 
7
10
C = -1570    (3)
- 
3
10
D = -1650    (4)
 
13
280
B + 
13
280
C + 
13
280
D - 
71
280
E = - 
1856
7
    (5)

Multiply both sides of equation (2) by 26, the equation can be obtained:
        - 
13
280
B - 
13
280
C - 
13
280
D - 
13
280
E = - 
10205
7
    (12)
, then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D - 
1
560
E = - 
785
14
    (2)
 
7
10
C = -1570    (3)
- 
3
10
D = -1650    (4)
- 
3
10
E = -1723    (5)

Divide both sides of equation (5) by 168, get the equation：
        - 
1
560
E = - 
1723
168
    (13)
, then subtract both sides of equation (13) from both sides of equation (2), get the equation：
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D + 
27
20
E = 530    (1)
- 
1
560
B - 
1
560
C - 
1
560
D = - 
7697
168
    (2)
 
7
10
C = -1570    (3)
- 
3
10
D = -1650    (4)
- 
3
10
E = -1723    (5)

Multiply both sides of equation (5) by 9
Divide both sides of equation (5) by 2, get the equation：
        - 
27
20
E = - 
15507
2
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D = - 
14447
2
    (1)
- 
1
560
B - 
1
560
C - 
1
560
D = - 
7697
168
    (2)
 
7
10
C = -1570    (3)
- 
3
10
D = -1650    (4)
- 
3
10
E = -1723    (5)

Divide both sides of equation (4) by 168, get the equation：
        - 
1
560
D = - 
275
28
    (15)
, then subtract both sides of equation (15) from both sides of equation (2), get the equation：
 
7
5
A + 
27
20
B + 
27
20
C + 
27
20
D = - 
14447
2
    (1)
- 
1
560
B - 
1
560
C = - 
6047
168
    (2)
 
7
10
C = -1570    (3)
- 
3
10
D = -1650    (4)
 E = 
17230
3
    (5)

Multiply both sides of equation (4) by 9
Divide both sides of equation (4) by 2, get the equation：
        - 
27
20
D = -7425    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 
7
5
A + 
27
20
B + 
27
20
C = - 
29297
2
    (1)
- 
1
560
B - 
1
560
C = - 
6047
168
    (2)
 
7
10
C = -1570    (3)
- 
3
10
D = -1650    (4)
 E = 
17230
3
    (5)

Divide both sides of equation (3) by 392, get the equation：
         
1
560
C = - 
785
196
    (17)
, then add the two sides of equation (17) to both sides of equation (2), get the equation：
 
7
5
A + 
27
20
B + 
27
20
C = - 
29297
2
    (1)
- 
1
560
B = - 
47039
1176
    (2)
 
7
10
C = -1570    (3)
 D = 5500    (4)
 E = 
17230
3
    (5)

Multiply both sides of equation (3) by 27
Divide both sides of equation (3) by 14, get the equation：
         
27
20
C = - 
21195
7
    (18)
, then subtract both sides of equation (18) from both sides of equation (1), get the equation：
 
7
5
A + 
27
20
B = - 
162689
14
    (1)
- 
1
560
B = - 
47039
1176
    (2)
 
7
10
C = -1570    (3)
 D = 5500    (4)
 E = 
17230
3
    (5)

Multiply both sides of equation (2) by 756, get the equation：
        - 
27
20
B = - 
423351
14
    (19)
, then add the two sides of equation (19) to both sides of equation (1), get the equation：
 
7
5
A = -41860    (1)
- 
1
560
B = - 
47039
1176
    (2)
 C = - 
15700
7
    (3)
 D = 5500    (4)
 E = 
17230
3
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = -29900    (1)
 B = 
470390
21
    (2)
 C = - 
15700
7
    (3)
 D = 5500    (4)
 E = 
17230
3
    (5)


Therefore, the solution of the equation set is:
A = -29900
B = 
470390
21
C = - 
15700
7
D = 5500
E = 
17230
3


Convert the solution of the equation set to decimals:
A = -29900
B = 22399.523810
C = -2242.857143
D = 5500
E = 5743.333333

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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