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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:
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 D + E = 2000    (3)
- 
3
10
A - 
3
10
B = 900    (4)
 
3
10
A + 
3
10
E = 0    (5)
 
3
10
A + 
3
10
C - 
3
10
F = 0    (6)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 10, the equation can be obtained:
         
3
10
A + 
3
10
C = - 
361089
2000
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 D + E = 2000    (3)
- 
3
10
B + 
3
10
C = 
1438911
2000
    (4)
 
3
10
A + 
3
10
E = 0    (5)
 
3
10
A + 
3
10
C - 
3
10
F = 0    (6)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 10, the equation can be obtained:
         
3
10
A + 
3
10
C = - 
361089
2000
    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 D + E = 2000    (3)
- 
3
10
B + 
3
10
C = 
1438911
2000
    (4)
- 
3
10
C + 
3
10
E = 
361089
2000
    (5)
 
3
10
A + 
3
10
C - 
3
10
F = 0    (6)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 10, the equation can be obtained:
         
3
10
A + 
3
10
C = - 
361089
2000
    (9)
, then subtract both sides of equation (9) from both sides of equation (6), the equations are reduced to:
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 D + E = 2000    (3)
- 
3
10
B + 
3
10
C = 
1438911
2000
    (4)
- 
3
10
C + 
3
10
E = 
361089
2000
    (5)
- 
3
10
F = 
361089
2000
    (6)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 10, the equation can be obtained:
         
3
10
B + 
3
10
F = 
120819
2000
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 D + E = 2000    (3)
 
3
10
C + 
3
10
F = 
155973
200
    (4)
- 
3
10
C + 
3
10
E = 
361089
2000
    (5)
- 
3
10
F = 
361089
2000
    (6)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 
3
10
C + 
3
10
F = 
155973
200
    (3)
 D + E = 2000    (4)
- 
3
10
C + 
3
10
E = 
361089
2000
    (5)
- 
3
10
F = 
361089
2000
    (6)

Add both sides of equation (3) to both sides of equation (5) ,the equations are reduced to:
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 
3
10
C + 
3
10
F = 
155973
200
    (3)
 D + E = 2000    (4)
 
3
10
E + 
3
10
F = 
1920819
2000
    (5)
- 
3
10
F = 
361089
2000
    (6)

Add both sides of equation (6) to both sides of equation (5), get the equation：
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 
3
10
C + 
3
10
F = 
155973
200
    (3)
 D + E = 2000    (4)
 
3
10
E = 
570477
500
    (5)
- 
3
10
F = 
361089
2000
    (6)

Add both sides of equation (6) to both sides of equation (3), get the equation：
 A + C = - 
120363
200
    (1)
 B + F = 
40273
200
    (2)
 
3
10
C = 
1920819
2000
    (3)
 D + E = 2000    (4)
 
3
10
E = 
570477
500
    (5)
- 
3
10
F = 
361089
2000
    (6)

Multiply both sides of equation (6) by 10
Divide both sides of equation (6) by 3, get the equation：
        -1F = 
120363
200
    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 A + C = - 
120363
200
    (1)
 B = 
40159
50
    (2)
 
3
10
C = 
1920819
2000
    (3)
 D + E = 2000    (4)
 
3
10
E = 
570477
500
    (5)
- 
3
10
F = 
361089
2000
    (6)

Multiply both sides of equation (5) by 10
Divide both sides of equation (5) by 3, get the equation：
         E = 
190159
50
    (12)
, then subtract both sides of equation (12) from both sides of equation (4), get the equation：
 A + C = - 
120363
200
    (1)
 B = 
40159
50
    (2)
 
3
10
C = 
1920819
2000
    (3)
 D = - 
90159
50
    (4)
 
3
10
E = 
570477
500
    (5)
 F = - 
120363
200
    (6)

Multiply both sides of equation (3) by 10
Divide both sides of equation (3) by 3, get the equation：
         C = 
640273
200
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 A = - 
190159
50
    (1)
 B = 
40159
50
    (2)
 
3
10
C = 
1920819
2000
    (3)
 D = - 
90159
50
    (4)
 E = 
190159
50
    (5)
 F = - 
120363
200
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
190159
50
    (1)
 B = 
40159
50
    (2)
 C = 
640273
200
    (3)
 D = - 
90159
50
    (4)
 E = 
190159
50
    (5)
 F = - 
120363
200
    (6)


Therefore, the solution of the equation set is:
A = - 
190159
50
B = 
40159
50
C = 
640273
200
D = - 
90159
50
E = 
190159
50
F = - 
120363
200


Convert the solution of the equation set to decimals:
A = -3803.180000
B = 803.180000
C = 3201.365000
D = -1803.180000
E = 3803.180000
F = -601.815000

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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