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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:
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
3
5
A + 
3
5
B + 
3
5
C + 
3
5
D = 
3
5
    (2)
 
3
5
A + 
3
5
B + 
3
5
C = 
3
5
    (3)
 
3
5
A + 
3
5
D = 
3
5
    (4)
Question solving process:

Multiply both sides of equation (1) by 200
Divide the two sides of equation (1) by 169, the equation can be obtained:
         
3
5
A + 
100
169
B + 
120
169
C + 
120
169
D = 
120
169
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C - 
93
845
D = - 
93
845
    (2)
 
3
5
A + 
3
5
B + 
3
5
C = 
3
5
    (3)
 
3
5
A + 
3
5
D = 
3
5
    (4)

Multiply both sides of equation (1) by 200
Divide the two sides of equation (1) by 169, the equation can be obtained:
         
3
5
A + 
100
169
B + 
120
169
C + 
120
169
D = 
120
169
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C - 
93
845
D = - 
93
845
    (2)
 
7
845
B - 
93
845
C - 
120
169
D = - 
93
845
    (3)
 
3
5
A + 
3
5
D = 
3
5
    (4)

Multiply both sides of equation (1) by 200
Divide the two sides of equation (1) by 169, the equation can be obtained:
         
3
5
A + 
100
169
B + 
120
169
C + 
120
169
D = 
120
169
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C - 
93
845
D = - 
93
845
    (2)
 
7
845
B - 
93
845
C - 
120
169
D = - 
93
845
    (3)
- 
100
169
B - 
120
169
C - 
93
845
D = - 
93
845
    (4)

Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C - 
93
845
D = - 
93
845
    (2)
- 
3
5
D = 0    (3)
- 
100
169
B - 
120
169
C - 
93
845
D = - 
93
845
    (4)

Multiply both sides of equation (2) by 500
Divide the two sides of equation (2) by 7, the equation can be obtained:
         
100
169
B - 
9300
1183
C - 
9300
1183
D = - 
9300
1183
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C - 
93
845
D = - 
93
845
    (2)
- 
3
5
D = 0    (3)
- 
60
7
C - 
279
35
D = - 
279
35
    (4)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C - 
93
845
D = - 
93
845
    (2)
- 
60
7
C - 
279
35
D = - 
279
35
    (3)
- 
3
5
D = 0    (4)

Multiply both sides of equation (4) by 93
Divide both sides of equation (4) by 7, get the equation：
        - 
279
35
D = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (3), get the equation：
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C - 
93
845
D = - 
93
845
    (2)
- 
60
7
C = - 
279
35
    (3)
- 
3
5
D = 0    (4)

Multiply both sides of equation (4) by 31
Divide both sides of equation (4) by 169, get the equation：
        - 
93
845
D = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (2), get the equation：
 
507
1000
A + 
1
2
B + 
3
5
C + 
3
5
D = 
3
5
    (1)
 
7
845
B - 
93
845
C = - 
93
845
    (2)
- 
60
7
C = - 
279
35
    (3)
- 
3
5
D = 0    (4)

Add both sides of equation (4) to both sides of equation (1), get the equation：
 
507
1000
A + 
1
2
B + 
3
5
C = 
3
5
    (1)
 
7
845
B - 
93
845
C = - 
93
845
    (2)
- 
60
7
C = - 
279
35
    (3)
- 
3
5
D = 0    (4)

Multiply both sides of equation (3) by 217
Divide both sides of equation (3) by 16900, get the equation：
        - 
93
845
C = - 
8649
84500
    (11)
, then subtract both sides of equation (11) from both sides of equation (2), get the equation：
 
507
1000
A + 
1
2
B + 
3
5
C = 
3
5
    (1)
 
7
845
B = - 
651
84500
    (2)
- 
60
7
C = - 
279
35
    (3)
 D = 0    (4)

Multiply both sides of equation (3) by 7
Divide both sides of equation (3) by 100, get the equation：
        - 
3
5
C = - 
279
500
    (12)
, then add the two sides of equation (12) to both sides of equation (1), get the equation：
 
507
1000
A + 
1
2
B = 
21
500
    (1)
 
7
845
B = - 
651
84500
    (2)
- 
60
7
C = - 
279
35
    (3)
 D = 0    (4)

Multiply both sides of equation (2) by 845
Divide both sides of equation (2) by 14, get the equation：
         
1
2
B = - 
93
200
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 
507
1000
A = 
507
1000
    (1)
 
7
845
B = - 
651
84500
    (2)
 C = 
93
100
    (3)
 D = 0    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 1    (1)
 B = - 
93
100
    (2)
 C = 
93
100
    (3)
 D = 0    (4)


Therefore, the solution of the equation set is:
A = 1
B = - 
93
100
C = 
93
100
D = 0


Convert the solution of the equation set to decimals:
A = 1
B = -0.930000
C = 0.930000
D = 0

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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