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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:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (2)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (3)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (4)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (5)
Question solving process:

Multiply both sides of equation (1) by 199
Divide the two sides of equation (1) by 111, the equation can be obtained:
         
199
100
A + 
39601
11100
B + 
59501
11100
C + 
26467
3700
D + 
1990
111
E = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (3)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (4)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (5)

Multiply both sides of equation (1) by 199
Divide the two sides of equation (1) by 111, the equation can be obtained:
         
199
100
A + 
39601
11100
B + 
59501
11100
C + 
26467
3700
D + 
1990
111
E = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (3)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (4)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (5)

Multiply both sides of equation (1) by 199
Divide the two sides of equation (1) by 111, the equation can be obtained:
         
199
100
A + 
39601
11100
B + 
59501
11100
C + 
26467
3700
D + 
1990
111
E = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (3)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (4)
 
199
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (5)

Multiply both sides of equation (1) by 199
Divide the two sides of equation (1) by 111, the equation can be obtained:
         
199
100
A + 
39601
11100
B + 
59501
11100
C + 
26467
3700
D + 
1990
111
E = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (3)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (4)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (5)

Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
0 = 0    (3)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (4)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (5)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
0 = 0    (3)
0 = 0    (4)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (5)

Subtract both sides of equation (2) from both sides of equation (5) ,the equations are reduced to:
 
111
100
A + 
199
100
B + 
299
100
C + 
399
100
D + 10E = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
0 = 0    (3)
0 = 0    (4)
0 = 0    (5)

Multiply both sides of equation (2) by 22089
Divide both sides of equation (2) by 17512, get the equation：
        - 
39601
19900
B - 
59501
19900
C - 
79401
19900
D - 
1990
199
E = 0    (10)
, then add the two sides of equation (10) to both sides of equation (1), get the equation：
 
111
100
A = 0    (1)
- 
4378
2775
B - 
6578
2775
C - 
2926
925
D - 
880
111
E = 0    (2)
0 = 0    (3)
0 = 0    (4)
0 = 0    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 0    (1)
 B + 
299
199
C + 
399
199
D + 
1000
199
E = 0    (2)
0 = 0    (3)
0 = 0    (4)
0 = 0    (5)


Therefore, the solution of the equation set is:
A = 0
B = -
299
199
C - 
399
199
D - 
1000
199
E

Where:  C, D, E 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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