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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 + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
 A + 
7
100
B + 
7
100
C + 
107
100
D + 
107
100
E -1F = 0    (2)
 A + 
7
100
B + 
7
100
C + E -1F = 0    (3)
 A -1F = 0    (4)
 A -1F = 0    (5)
 A -1F = 0    (6)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
 A + 
7
100
B + 
7
100
C + E -1F = 0    (3)
 A -1F = 0    (4)
 A -1F = 0    (5)
 A -1F = 0    (6)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
11
10
B - 
2
5
C - 
107
100
D - 
7
100
E = 0    (3)
 A -1F = 0    (4)
 A -1F = 0    (5)
 A -1F = 0    (6)

Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
11
10
B - 
2
5
C - 
107
100
D - 
7
100
E = 0    (3)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (4)
 A -1F = 0    (5)
 A -1F = 0    (6)

Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
11
10
B - 
2
5
C - 
107
100
D - 
7
100
E = 0    (3)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (4)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (5)
 A -1F = 0    (6)

Subtract both sides of equation (1) from both sides of equation (6) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
11
10
B - 
2
5
C - 
107
100
D - 
7
100
E = 0    (3)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (4)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (5)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (6)

Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
107
100
D - 
7
100
E = 0    (3)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (4)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (5)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (6)

Multiply both sides of equation (2) by 117
Divide the two sides of equation (2) by 110, the equation can be obtained:
        - 
117
100
B - 
117
275
C = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
107
100
D - 
7
100
E = 0    (3)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (4)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (5)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (6)

Multiply both sides of equation (2) by 117
Divide the two sides of equation (2) by 110, the equation can be obtained:
        - 
117
100
B - 
117
275
C = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
107
100
D - 
7
100
E = 0    (3)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (4)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (5)
- 
117
100
B - 
47
100
C - 
107
100
D - 
107
100
E = 0    (6)

Multiply both sides of equation (2) by 117
Divide the two sides of equation (2) by 110, the equation can be obtained:
        - 
117
100
B - 
117
275
C = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (6), the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
107
100
D - 
7
100
E = 0    (3)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (4)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (5)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (6)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (3)
- 
107
100
D - 
7
100
E = 0    (4)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (5)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (6)

Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (3)
- 
107
100
D - 
7
100
E = 0    (4)
0 = 0    (5)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (6)

Subtract both sides of equation (3) from both sides of equation (6) ,the equations are reduced to:
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
49
1100
C - 
107
100
D - 
107
100
E = 0    (3)
- 
107
100
D - 
7
100
E = 0    (4)
0 = 0    (5)
0 = 0    (6)

Subtract both sides of equation (4) from both sides of equation (3), get the equation：
 A + 
117
100
B + 
47
100
C + 
107
100
D + 
107
100
E -1F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
49
1100
C - 
107
107
E = 0    (3)
- 
107
100
D - 
7
100
E = 0    (4)
0 = 0    (5)
0 = 0    (6)

Add both sides of equation (4) to both sides of equation (1), get the equation：
 A + 
117
100
B + 
47
100
C + E - 
107
107
F = 0    (1)
- 
11
10
B - 
2
5
C = 0    (2)
- 
49
1100
C - 
107
107
E = 0    (3)
- 
107
100
D - 
7
100
E = 0    (4)
0 = 0    (5)
0 = 0    (6)

Multiply both sides of equation (3) by 440
Divide both sides of equation (3) by 49, get the equation：
        - 
2
5
C - 
47080
5243
E = 0    (10)
, then subtract both sides of equation (10) from both sides of equation (2), get the equation：
 A + 
117
100
B + 
47
100
C + E - 
107
107
F = 0    (1)
- 
11
10
B + 
47080
5243
E = 0    (2)
- 
49
1100
C - 
107
107
E = 0    (3)
 D + 
7
107
E = 0    (4)
0 = 0    (5)
0 = 0    (6)

Multiply both sides of equation (3) by 517
Divide both sides of equation (3) by 49, get the equation：
        - 
47
100
C - 
55319
5243
E = 0    (11)
, then add the two sides of equation (11) to both sides of equation (1), get the equation：
 A + 
117
100
B - 
50076
5243
E - 
107
107
F = 0    (1)
- 
11
10
B + 
47080
5243
E = 0    (2)
- 
49
1100
C - 
107
107
E = 0    (3)
 D + 
7
107
E = 0    (4)
0 = 0    (5)
0 = 0    (6)

Multiply both sides of equation (2) by 117
Divide both sides of equation (2) by 110, get the equation：
        - 
117
100
B + 
50076
5243
E = 0    (12)
, then add the two sides of equation (12) to both sides of equation (1), get the equation：
 A - 
107
107
F = 0    (1)
- 
11
10
B + 
47080
5243
E = 0    (2)
 C + 
117700
5243
E = 0    (3)
 D + 
7
107
E = 0    (4)
0 = 0    (5)
0 = 0    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A - 
107
107
F = 0    (1)
 B - 
42800
5243
E = 0    (2)
 C + 
117700
5243
E = 0    (3)
 D + 
7
107
E = 0    (4)
0 = 0    (5)
0 = 0    (6)


Therefore, the solution of the equation set is:
A = 
107
107
F
B = 
42800
5243
E
C = -
117700
5243
E
D = -
7
107
E

Where:  E, F 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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