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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 + B + C + D + E = 0    (1)
 16A + 8B + 4C + 2D + E = -29    (2)
 8A + 27B + 9C + 3D + E = -237    (3)
 256A + 64B + 16C + 4D + E = -1014    (4)
 625A + 125B + 25C + 5D + E = -3110    (5)
Question solving process:

Multiply both sides of equation (1) by 16, the equation can be obtained:
         16A + 16B + 16C + 16D + 16E = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
 8A + 27B + 9C + 3D + E = -237    (3)
 256A + 64B + 16C + 4D + E = -1014    (4)
 625A + 125B + 25C + 5D + E = -3110    (5)

Multiply both sides of equation (1) by 8, the equation can be obtained:
         8A + 8B + 8C + 8D + 8E = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
 19B + C -5D -7E = -237    (3)
 256A + 64B + 16C + 4D + E = -1014    (4)
 625A + 125B + 25C + 5D + E = -3110    (5)

Multiply both sides of equation (1) by 256, the equation can be obtained:
         256A + 256B + 256C + 256D + 256E = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
 19B + C -5D -7E = -237    (3)
-192B -240C -252D -255E = -1014    (4)
 625A + 125B + 25C + 5D + E = -3110    (5)

Multiply both sides of equation (1) by 625, the equation can be obtained:
         625A + 625B + 625C + 625D + 625E = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
 19B + C -5D -7E = -237    (3)
-192B -240C -252D -255E = -1014    (4)
-500B -600C -620D -624E = -3110    (5)

Multiply both sides of equation (2) by 19
Divide the two sides of equation (2) by 8, the equation can be obtained:
        -19B - 
57
2
C - 
133
4
D - 
285
8
E = - 
551
8
    (10)
, then add the two sides of equation (10) to both sides of equation (3), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D - 
341
8
E = - 
2447
8
    (3)
-192B -240C -252D -255E = -1014    (4)
-500B -600C -620D -624E = -3110    (5)

Multiply both sides of equation (2) by 24, the equation can be obtained:
        -192B -288C -336D -360E = -696    (11)
, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D - 
341
8
E = - 
2447
8
    (3)
 48C + 84D + 105E = -318    (4)
-500B -600C -620D -624E = -3110    (5)

Multiply both sides of equation (2) by 125
Divide the two sides of equation (2) by 2, the equation can be obtained:
        -500B -750C -875D - 
1875
2
E = - 
3625
2
    (12)
, then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D - 
341
8
E = - 
2447
8
    (3)
 48C + 84D + 105E = -318    (4)
 150C + 255D + 
627
2
E = - 
2595
2
    (5)

Multiply both sides of equation (3) by 96
Divide the two sides of equation (3) by 55, the equation can be obtained:
        -48C - 
3672
55
D - 
372
5
E = - 
29364
55
    (13)
, then add the two sides of equation (13) to both sides of equation (4), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D - 
341
8
E = - 
2447
8
    (3)
 
948
55
D + 
153
5
E = - 
46854
55
    (4)
 150C + 255D + 
627
2
E = - 
2595
2
    (5)

Multiply both sides of equation (3) by 60
Divide the two sides of equation (3) by 11, the equation can be obtained:
        -150C - 
2295
11
D - 
465
2
E = - 
36705
22
    (14)
, then add the two sides of equation (14) to both sides of equation (5), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D - 
341
8
E = - 
2447
8
    (3)
 
948
55
D + 
153
5
E = - 
46854
55
    (4)
 
510
11
D + 81E = - 
32625
11
    (5)

Multiply both sides of equation (4) by 425
Divide the two sides of equation (4) by 158, the equation can be obtained:
         
510
11
D + 
13005
158
E = - 
1991295
869
    (15)
, then subtract both sides of equation (15) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D - 
341
8
E = - 
2447
8
    (3)
 
948
55
D + 
153
5
E = - 
46854
55
    (4)
- 
207
158
E = - 
53280
79
    (5)

Multiply both sides of equation (5) by 2686
Divide both sides of equation (5) by 115, get the equation：
        - 
3519
115
E = - 
362304
23
    (16)
, then add the two sides of equation (16) to both sides of equation (4), get the equation：
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D - 
341
8
E = - 
2447
8
    (3)
 
948
55
D = - 
21004362
1265
    (4)
- 
207
158
E = - 
53280
79
    (5)

Multiply both sides of equation (5) by 26939
Divide both sides of equation (5) by 828, get the equation：
        - 
26939
632
E = - 
504680
23
    (17)
, then subtract both sides of equation (17) from both sides of equation (3), get the equation：
 A + B + C + D + E = 0    (1)
-8B -12C -14D -15E = -29    (2)
- 
55
2
C - 
153
4
D = 
3981159
184
    (3)
 
948
55
D = - 
21004362
1265
    (4)
- 
207
158
E = - 
53280
79
    (5)

Multiply both sides of equation (5) by 790
Divide both sides of equation (5) by 69, get the equation：
        -15E = - 
177600
23
    (18)
, then subtract both sides of equation (18) from both sides of equation (2), get the equation：
 A + B + C + D + E = 0    (1)
-8B -12C -14D = 
176933
23
    (2)
- 
55
2
C - 
153
4
D = 
3981159
184
    (3)
 
948
55
D = - 
21004362
1265
    (4)
- 
207
158
E = - 
53280
79
    (5)

Multiply both sides of equation (5) by 158
Divide both sides of equation (5) by 207, get the equation：
        -1E = - 
11840
23
    (19)
, then add the two sides of equation (19) to both sides of equation (1), get the equation：
 A + B + C + D = - 
11840
23
    (1)
-8B -12C -14D = 
176933
23
    (2)
- 
55
2
C - 
153
4
D = 
3981159
184
    (3)
 
948
55
D = - 
21004362
1265
    (4)
- 
207
158
E = - 
53280
79
    (5)

Multiply both sides of equation (4) by 2805
Divide both sides of equation (4) by 1264, get the equation：
         
12087
316
D = - 
6779889
184
    (20)
, then add the two sides of equation (20) to both sides of equation (3), get the equation：
 A + B + C + D = - 
11840
23
    (1)
-8B -12C -14D = 
176933
23
    (2)
- 
55
2
C = - 
1399365
92
    (3)
 
948
55
D = - 
21004362
1265
    (4)
 E = 
11840
23
    (5)

Multiply both sides of equation (4) by 385
Divide both sides of equation (4) by 474, get the equation：
         14D = - 
310191
23
    (21)
, then add the two sides of equation (21) to both sides of equation (2), get the equation：
 A + B + C + D = - 
11840
23
    (1)
-8B -12C = - 
133258
23
    (2)
- 
55
2
C = - 
1399365
92
    (3)
 
948
55
D = - 
21004362
1265
    (4)
 E = 
11840
23
    (5)

Multiply both sides of equation (4) by 55
Divide both sides of equation (4) by 948, get the equation：
         D = - 
3500727
3634
    (22)
, then subtract both sides of equation (22) from both sides of equation (1), get the equation：
 A + B + C = 
1630007
3634
    (1)
-8B -12C = - 
133258
23
    (2)
- 
55
2
C = - 
1399365
92
    (3)
 
948
55
D = - 
21004362
1265
    (4)
 E = 
11840
23
    (5)

Multiply both sides of equation (3) by 24
Divide both sides of equation (3) by 55, get the equation：
        -12C = - 
152658
23
    (23)
, then subtract both sides of equation (23) from both sides of equation (2), get the equation：
 A + B + C = 
1630007
3634
    (1)
-8B = 
19400
23
    (2)
- 
55
2
C = - 
1399365
92
    (3)
 D = - 
3500727
3634
    (4)
 E = 
11840
23
    (5)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 55, get the equation：
        -1C = - 
25443
46
    (24)
, then add the two sides of equation (24) to both sides of equation (1), get the equation：
 A + B = - 
189995
1817
    (1)
-8B = 
19400
23
    (2)
- 
55
2
C = - 
1399365
92
    (3)
 D = - 
3500727
3634
    (4)
 E = 
11840
23
    (5)

Divide both sides of equation (2) by 8, get the equation：
        -1B = 
2425
23
    (25)
, then add the two sides of equation (25) to both sides of equation (1), get the equation：
 A = 
1580
1817
    (1)
-8B = 
19400
23
    (2)
 C = 
25443
46
    (3)
 D = - 
3500727
3634
    (4)
 E = 
11840
23
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
1580
1817
    (1)
 B = - 
2425
23
    (2)
 C = 
25443
46
    (3)
 D = - 
3500727
3634
    (4)
 E = 
11840
23
    (5)


Therefore, the solution of the equation set is:
A = 
1580
1817
B = - 
2425
23
C = 
25443
46
D = - 
3500727
3634
E = 
11840
23


Convert the solution of the equation set to decimals:
A = 0.869565
B = -105.434783
C = 553.108696
D = -963.326087
E = 514.782609

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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