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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 + F = 2    (1)
 32A + 16B + 8C + 4D + 2E + F = 4    (2)
 243A + 81B + 27C + 9D + 3E + F = 6    (3)
 1024A + 256B + 64C + 16D + 4E + F = 7    (4)
 3125A + 625B + 125C + 25D + 5E + F = 8    (5)
 216A + 216B + 216C + 36D + 6E + F = 24678    (6)
Question solving process:

Multiply both sides of equation (1) by 32, the equation can be obtained:
         32A + 32B + 32C + 32D + 32E + 32F = 64    (7)
, then subtract both sides of equation (7) from both sides of equation (2), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 243A + 81B + 27C + 9D + 3E + F = 6    (3)
 1024A + 256B + 64C + 16D + 4E + F = 7    (4)
 3125A + 625B + 125C + 25D + 5E + F = 8    (5)
 216A + 216B + 216C + 36D + 6E + F = 24678    (6)

Multiply both sides of equation (1) by 243, the equation can be obtained:
         243A + 243B + 243C + 243D + 243E + 243F = 486    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
-162B -216C -234D -240E -242F = -480    (3)
 1024A + 256B + 64C + 16D + 4E + F = 7    (4)
 3125A + 625B + 125C + 25D + 5E + F = 8    (5)
 216A + 216B + 216C + 36D + 6E + F = 24678    (6)

Multiply both sides of equation (1) by 1024, the equation can be obtained:
         1024A + 1024B + 1024C + 1024D + 1024E + 1024F = 2048    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
-162B -216C -234D -240E -242F = -480    (3)
-768B -960C -1008D -1020E -1023F = -2041    (4)
 3125A + 625B + 125C + 25D + 5E + F = 8    (5)
 216A + 216B + 216C + 36D + 6E + F = 24678    (6)

Multiply both sides of equation (1) by 3125, the equation can be obtained:
         3125A + 3125B + 3125C + 3125D + 3125E + 3125F = 6250    (10)
, then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
-162B -216C -234D -240E -242F = -480    (3)
-768B -960C -1008D -1020E -1023F = -2041    (4)
-2500B -3000C -3100D -3120E -3124F = -6242    (5)
 216A + 216B + 216C + 36D + 6E + F = 24678    (6)

Multiply both sides of equation (1) by 216, the equation can be obtained:
         216A + 216B + 216C + 216D + 216E + 216F = 432    (11)
, then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
-162B -216C -234D -240E -242F = -480    (3)
-768B -960C -1008D -1020E -1023F = -2041    (4)
-2500B -3000C -3100D -3120E -3124F = -6242    (5)
-180D -210E -215F = 24246    (6)

Multiply both sides of equation (2) by 81
Divide the two sides of equation (2) by 8, the equation can be obtained:
        -162B -243C - 
567
2
D - 
1215
4
E - 
2511
8
F = - 
1215
2
    (12)
, then subtract both sides of equation (12) from both sides of equation (3), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-768B -960C -1008D -1020E -1023F = -2041    (4)
-2500B -3000C -3100D -3120E -3124F = -6242    (5)
-180D -210E -215F = 24246    (6)

Multiply both sides of equation (2) by 48, the equation can be obtained:
        -768B -1152C -1344D -1440E -1488F = -2880    (13)
, then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
 192C + 336D + 420E + 465F = 839    (4)
-2500B -3000C -3100D -3120E -3124F = -6242    (5)
-180D -210E -215F = 24246    (6)

Multiply both sides of equation (2) by 625
Divide the two sides of equation (2) by 4, the equation can be obtained:
        -2500B -3750C -4375D - 
9375
2
E - 
19375
4
F = -9375    (14)
, then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
 192C + 336D + 420E + 465F = 839    (4)
 750C + 1275D + 
3135
2
E + 
6879
4
F = 3133    (5)
-180D -210E -215F = 24246    (6)

Multiply both sides of equation (3) by 64
Divide the two sides of equation (3) by 9, the equation can be obtained:
         192C + 352D + 
1360
3
E + 
4600
9
F = 
2720
3
    (15)
, then subtract both sides of equation (15) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-16D - 
100
3
E - 
415
9
F = - 
203
3
    (4)
 750C + 1275D + 
3135
2
E + 
6879
4
F = 3133    (5)
-180D -210E -215F = 24246    (6)

Multiply both sides of equation (3) by 250
Divide the two sides of equation (3) by 9, the equation can be obtained:
         750C + 1375D + 
10625
6
E + 
71875
36
F = 
10625
3
    (16)
, then subtract both sides of equation (16) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-16D - 
100
3
E - 
415
9
F = - 
203
3
    (4)
-100D - 
610
3
E - 
2491
9
F = - 
1226
3
    (5)
-180D -210E -215F = 24246    (6)

Multiply both sides of equation (4) by 25
Divide the two sides of equation (4) by 4, the equation can be obtained:
        -100D - 
625
3
E - 
10375
36
F = - 
5075
12
    (17)
, then subtract both sides of equation (17) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-16D - 
100
3
E - 
415
9
F = - 
203
3
    (4)
 5E + 
137
12
F = 
57
4
    (5)
-180D -210E -215F = 24246    (6)

Multiply both sides of equation (4) by 45
Divide the two sides of equation (4) by 4, the equation can be obtained:
        -180D -375E - 
2075
4
F = - 
3045
4
    (18)
, then subtract both sides of equation (18) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-16D - 
100
3
E - 
415
9
F = - 
203
3
    (4)
 5E + 
137
12
F = 
57
4
    (5)
 165E + 
1215
4
F = 
100029
4
    (6)

Multiply both sides of equation (5) by 33, the equation can be obtained:
         165E + 
1507
4
F = 
1881
4
    (19)
, then subtract both sides of equation (19) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-16D - 
100
3
E - 
415
9
F = - 
203
3
    (4)
 5E + 
137
12
F = 
57
4
    (5)
-73F = 24537    (6)

Multiply both sides of equation (6) by 137
Divide both sides of equation (6) by 876, get the equation：
        - 
137
12
F = 
1120523
292
    (20)
, then add the two sides of equation (20) to both sides of equation (5), get the equation：
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-16D - 
100
3
E - 
415
9
F = - 
203
3
    (4)
 5E = 
281171
73
    (5)
-73F = 24537    (6)

Multiply both sides of equation (6) by 415
Divide both sides of equation (6) by 657, get the equation：
        - 
415
9
F = 
3394285
219
    (21)
, then subtract both sides of equation (21) from both sides of equation (4), get the equation：
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E + 
575
8
F = 
255
2
    (3)
-16D - 
100
3
E = - 
1136368
73
    (4)
 5E = 
281171
73
    (5)
-73F = 24537    (6)

Multiply both sides of equation (6) by 575
Divide both sides of equation (6) by 584, get the equation：
        - 
575
8
F = 
14108775
584
    (22)
, then add the two sides of equation (22) to both sides of equation (3), get the equation：
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E -31F = -60    (2)
 27C + 
99
2
D + 
255
4
E = 
14183235
584
    (3)
-16D - 
100
3
E = - 
1136368
73
    (4)
 5E = 
281171
73
    (5)
-73F = 24537    (6)

Multiply both sides of equation (6) by 31
Divide both sides of equation (6) by 73, get the equation：
        -31F = 
760647
73
    (23)
, then subtract both sides of equation (23) from both sides of equation (2), get the equation：
 A + B + C + D + E + F = 2    (1)
-16B -24C -28D -30E = - 
765027
73
    (2)
 27C + 
99
2
D + 
255
4
E = 
14183235
584
    (3)
-16D - 
100
3
E = - 
1136368
73
    (4)
 5E = 
281171
73
    (5)
-73F = 24537    (6)

Divide both sides of equation (6) by 73, get the equation：
        -1F = 
24537
73
    (24)
, then add the two sides of equation (24) to both sides of equation (1), get the equation：
 A + B + C + D + E = 
24683
73
    (1)
-16B -24C -28D -30E = - 
765027
73
    (2)
 27C + 
99
2
D + 
255
4
E = 
14183235
584
    (3)
-16D - 
100
3
E = - 
1136368
73
    (4)
 5E = 
281171
73
    (5)
-73F = 24537    (6)

Multiply both sides of equation (5) by 20
Divide both sides of equation (5) by 3, get the equation：
         
100
3
E = 
5623420
219
    (25)
, then add the two sides of equation (25) to both sides of equation (4), get the equation：
 A + B + C + D + E = 
24683
73
    (1)
-16B -24C -28D -30E = - 
765027
73
    (2)
 27C + 
99
2
D + 
255
4
E = 
14183235
584
    (3)
-16D = 
2214316
219
    (4)
 5E = 
281171
73
    (5)
 F = - 
24537
73
    (6)

Multiply both sides of equation (5) by 51
Divide both sides of equation (5) by 4, get the equation：
         
255
4
E = 
14339721
292
    (26)
, then subtract both sides of equation (26) from both sides of equation (3), get the equation：
 A + B + C + D + E = 
24683
73
    (1)
-16B -24C -28D -30E = - 
765027
73
    (2)
 27C + 
99
2
D = - 
14496207
584
    (3)
-16D = 
2214316
219
    (4)
 5E = 
281171
73
    (5)
 F = - 
24537
73
    (6)

Multiply both sides of equation (5) by 6, get the equation：
         30E = 
1687026
73
    (27)
, then add the two sides of equation (27) to both sides of equation (2), get the equation：
 A + B + C + D + E = 
24683
73
    (1)
-16B -24C -28D = 
921999
73
    (2)
 27C + 
99
2
D = - 
14496207
584
    (3)
-16D = 
2214316
219
    (4)
 5E = 
281171
73
    (5)
 F = - 
24537
73
    (6)

Divide both sides of equation (5) by 5, get the equation：
         E = 
281171
365
    (28)
, then subtract both sides of equation (28) from both sides of equation (1), get the equation：
 A + B + C + D = - 
157756
365
    (1)
-16B -24C -28D = 
921999
73
    (2)
 27C + 
99
2
D = - 
14496207
584
    (3)
-16D = 
2214316
219
    (4)
 5E = 
281171
73
    (5)
 F = - 
24537
73
    (6)

Multiply both sides of equation (4) by 99
Divide both sides of equation (4) by 32, get the equation：
        - 
99
2
D = 
18268107
584
    (29)
, then add the two sides of equation (29) to both sides of equation (3), get the equation：
 A + B + C + D = - 
157756
365
    (1)
-16B -24C -28D = 
921999
73
    (2)
 27C = 
942975
146
    (3)
-16D = 
2214316
219
    (4)
 E = 
281171
365
    (5)
 F = - 
24537
73
    (6)

Multiply both sides of equation (4) by 7
Divide both sides of equation (4) by 4, get the equation：
        -28D = 
3875053
219
    (30)
, then subtract both sides of equation (30) from both sides of equation (2), get the equation：
 A + B + C + D = - 
157756
365
    (1)
-16B -24C = - 
1109056
219
    (2)
 27C = 
942975
146
    (3)
-16D = 
2214316
219
    (4)
 E = 
281171
365
    (5)
 F = - 
24537
73
    (6)

Divide both sides of equation (4) by 16, get the equation：
        -1D = 
553579
876
    (31)
, then add the two sides of equation (31) to both sides of equation (1), get the equation：
 A + B + C = 
874823
4380
    (1)
-16B -24C = - 
1109056
219
    (2)
 27C = 
942975
146
    (3)
-16D = 
2214316
219
    (4)
 E = 
281171
365
    (5)
 F = - 
24537
73
    (6)

Multiply both sides of equation (3) by 8
Divide both sides of equation (3) by 9, get the equation：
         24C = 
419100
73
    (32)
, then add the two sides of equation (32) to both sides of equation (2), get the equation：
 A + B + C = 
874823
4380
    (1)
-16B = 
148244
219
    (2)
 27C = 
942975
146
    (3)
 D = - 
553579
876
    (4)
 E = 
281171
365
    (5)
 F = - 
24537
73
    (6)

Divide both sides of equation (3) by 27, get the equation：
         C = 
34925
146
    (33)
, then subtract both sides of equation (33) from both sides of equation (1), get the equation：
 A + B = - 
172927
4380
    (1)
-16B = 
148244
219
    (2)
 27C = 
942975
146
    (3)
 D = - 
553579
876
    (4)
 E = 
281171
365
    (5)
 F = - 
24537
73
    (6)

Divide both sides of equation (2) by 16, get the equation：
        -1B = 
37061
876
    (34)
, then add the two sides of equation (34) to both sides of equation (1), get the equation：
 A = 
2063
730
    (1)
-16B = 
148244
219
    (2)
 C = 
34925
146
    (3)
 D = - 
553579
876
    (4)
 E = 
281171
365
    (5)
 F = - 
24537
73
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
2063
730
    (1)
 B = - 
37061
876
    (2)
 C = 
34925
146
    (3)
 D = - 
553579
876
    (4)
 E = 
281171
365
    (5)
 F = - 
24537
73
    (6)


Therefore, the solution of the equation set is:
A = 
2063
730
B = - 
37061
876
C = 
34925
146
D = - 
553579
876
E = 
281171
365
F = - 
24537
73


Convert the solution of the equation set to decimals:
A = 2.826027
B = -42.307078
C = 239.212329
D = -631.939498
E = 770.331507
F = -336.123288

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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  New addition:Lenders ToolBox module（Specific location：Math OP > Lenders ToolBox ），welcome。