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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 + G = 2    (1)
 64A + 32B + 16C + 8D + 4E + 2F + G = 8    (2)
 729A + 243B + 81C + 27D + 9E + 3F + G = 20    (3)
 4096A + 1024B + 256C + 64D + 16E + 4F + G = 28    (4)
 15625A + 3125B + 625C + 125D + 25E + 5F + G = 50    (5)
 46656A + 7776B + 1296C + 216D + 36E + 6F + G = 82    (6)
 117649A + 16807B + 2401C + 343D + 49E + 7F + G = 126    (7)
Question solving process:

Multiply both sides of equation (1) by 64, the equation can be obtained:
         64A + 64B + 64C + 64D + 64E + 64F + 64G = 128    (8)
, then subtract both sides of equation (8) from both sides of equation (2), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 729A + 243B + 81C + 27D + 9E + 3F + G = 20    (3)
 4096A + 1024B + 256C + 64D + 16E + 4F + G = 28    (4)
 15625A + 3125B + 625C + 125D + 25E + 5F + G = 50    (5)
 46656A + 7776B + 1296C + 216D + 36E + 6F + G = 82    (6)
 117649A + 16807B + 2401C + 343D + 49E + 7F + G = 126    (7)

Multiply both sides of equation (1) by 729, the equation can be obtained:
         729A + 729B + 729C + 729D + 729E + 729F + 729G = 1458    (9)
, then subtract both sides of equation (9) from both sides of equation (3), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
-486B -648C -702D -720E -726F -728G = -1438    (3)
 4096A + 1024B + 256C + 64D + 16E + 4F + G = 28    (4)
 15625A + 3125B + 625C + 125D + 25E + 5F + G = 50    (5)
 46656A + 7776B + 1296C + 216D + 36E + 6F + G = 82    (6)
 117649A + 16807B + 2401C + 343D + 49E + 7F + G = 126    (7)

Multiply both sides of equation (1) by 4096, the equation can be obtained:
         4096A + 4096B + 4096C + 4096D + 4096E + 4096F + 4096G = 8192    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
-486B -648C -702D -720E -726F -728G = -1438    (3)
-3072B -3840C -4032D -4080E -4092F -4095G = -8164    (4)
 15625A + 3125B + 625C + 125D + 25E + 5F + G = 50    (5)
 46656A + 7776B + 1296C + 216D + 36E + 6F + G = 82    (6)
 117649A + 16807B + 2401C + 343D + 49E + 7F + G = 126    (7)

Multiply both sides of equation (1) by 15625, the equation can be obtained:
         15625A + 15625B + 15625C + 15625D + 15625E + 15625F + 15625G = 31250    (11)
, then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
-486B -648C -702D -720E -726F -728G = -1438    (3)
-3072B -3840C -4032D -4080E -4092F -4095G = -8164    (4)
-12500B -15000C -15500D -15600E -15620F -15624G = -31200    (5)
 46656A + 7776B + 1296C + 216D + 36E + 6F + G = 82    (6)
 117649A + 16807B + 2401C + 343D + 49E + 7F + G = 126    (7)

Multiply both sides of equation (1) by 46656, the equation can be obtained:
         46656A + 46656B + 46656C + 46656D + 46656E + 46656F + 46656G = 93312    (12)
, then subtract both sides of equation (12) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
-486B -648C -702D -720E -726F -728G = -1438    (3)
-3072B -3840C -4032D -4080E -4092F -4095G = -8164    (4)
-12500B -15000C -15500D -15600E -15620F -15624G = -31200    (5)
-38880B -45360C -46440D -46620E -46650F -46655G = -93230    (6)
 117649A + 16807B + 2401C + 343D + 49E + 7F + G = 126    (7)

Multiply both sides of equation (1) by 117649, the equation can be obtained:
         117649A + 117649B + 117649C + 117649D + 117649E + 117649F + 117649G = 235298    (13)
, then subtract both sides of equation (13) from both sides of equation (7), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
-486B -648C -702D -720E -726F -728G = -1438    (3)
-3072B -3840C -4032D -4080E -4092F -4095G = -8164    (4)
-12500B -15000C -15500D -15600E -15620F -15624G = -31200    (5)
-38880B -45360C -46440D -46620E -46650F -46655G = -93230    (6)
-100842B -115248C -117306D -117600E -117642F -117648G = -235172    (7)

Multiply both sides of equation (2) by 243
Divide the two sides of equation (2) by 16, the equation can be obtained:
        -486B -729C - 
1701
2
D - 
3645
4
E - 
7533
8
F - 
15309
16
G = - 
3645
2
    (14)
, then subtract both sides of equation (14) from both sides of equation (3), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-3072B -3840C -4032D -4080E -4092F -4095G = -8164    (4)
-12500B -15000C -15500D -15600E -15620F -15624G = -31200    (5)
-38880B -45360C -46440D -46620E -46650F -46655G = -93230    (6)
-100842B -115248C -117306D -117600E -117642F -117648G = -235172    (7)

Multiply both sides of equation (2) by 96, the equation can be obtained:
        -3072B -4608C -5376D -5760E -5952F -6048G = -11520    (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 + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
 768C + 1344D + 1680E + 1860F + 1953G = 3356    (4)
-12500B -15000C -15500D -15600E -15620F -15624G = -31200    (5)
-38880B -45360C -46440D -46620E -46650F -46655G = -93230    (6)
-100842B -115248C -117306D -117600E -117642F -117648G = -235172    (7)

Multiply both sides of equation (2) by 3125
Divide the two sides of equation (2) by 8, the equation can be obtained:
        -12500B -18750C -21875D - 
46875
2
E - 
96875
4
F - 
196875
8
G = -46875    (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 + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
 768C + 1344D + 1680E + 1860F + 1953G = 3356    (4)
 3750C + 6375D + 
15675
2
E + 
34395
4
F + 
71883
8
G = 15675    (5)
-38880B -45360C -46440D -46620E -46650F -46655G = -93230    (6)
-100842B -115248C -117306D -117600E -117642F -117648G = -235172    (7)

Multiply both sides of equation (2) by 1215, the equation can be obtained:
        -38880B -58320C -68040D -72900E -75330F -76545G = -145800    (17)
, then subtract both sides of equation (17) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
 768C + 1344D + 1680E + 1860F + 1953G = 3356    (4)
 3750C + 6375D + 
15675
2
E + 
34395
4
F + 
71883
8
G = 15675    (5)
 12960C + 21600D + 26280E + 28680F + 29890G = 52570    (6)
-100842B -115248C -117306D -117600E -117642F -117648G = -235172    (7)

Multiply both sides of equation (2) by 50421
Divide the two sides of equation (2) by 16, the equation can be obtained:
        -100842B -151263C - 
352947
2
D - 
756315
4
E - 
1563051
8
F - 
3176523
16
G = - 
756315
2
    (18)
, then subtract both sides of equation (18) from both sides of equation (7), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
 768C + 1344D + 1680E + 1860F + 1953G = 3356    (4)
 3750C + 6375D + 
15675
2
E + 
34395
4
F + 
71883
8
G = 15675    (5)
 12960C + 21600D + 26280E + 28680F + 29890G = 52570    (6)
 36015C + 
118335
2
D + 
285915
4
E + 
621915
8
F + 
1294155
16
G = 
285971
2
    (7)

Multiply both sides of equation (3) by 256
Divide the two sides of equation (3) by 27, the equation can be obtained:
         768C + 1408D + 
5440
3
E + 
18400
9
F + 
58576
27
G = 
98432
27
    (19)
, then subtract both sides of equation (19) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 3750C + 6375D + 
15675
2
E + 
34395
4
F + 
71883
8
G = 15675    (5)
 12960C + 21600D + 26280E + 28680F + 29890G = 52570    (6)
 36015C + 
118335
2
D + 
285915
4
E + 
621915
8
F + 
1294155
16
G = 
285971
2
    (7)

Multiply both sides of equation (3) by 1250
Divide the two sides of equation (3) by 27, the equation can be obtained:
         3750C + 6875D + 
53125
6
E + 
359375
36
F + 
2288125
216
G = 
480625
27
    (20)
, then subtract both sides of equation (20) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
-500D - 
3050
3
E - 
12455
9
F - 
86821
54
G = - 
57400
27
    (5)
 12960C + 21600D + 26280E + 28680F + 29890G = 52570    (6)
 36015C + 
118335
2
D + 
285915
4
E + 
621915
8
F + 
1294155
16
G = 
285971
2
    (7)

Multiply both sides of equation (3) by 160, the equation can be obtained:
         12960C + 23760D + 30600E + 34500F + 36610G = 61520    (21)
, then subtract both sides of equation (21) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
-500D - 
3050
3
E - 
12455
9
F - 
86821
54
G = - 
57400
27
    (5)
-2160D -4320E -5820F -6720G = -8950    (6)
 36015C + 
118335
2
D + 
285915
4
E + 
621915
8
F + 
1294155
16
G = 
285971
2
    (7)

Multiply both sides of equation (3) by 12005
Divide the two sides of equation (3) by 27, the equation can be obtained:
         36015C + 
132055
2
D + 
1020425
12
E + 
6902875
72
F + 
43950305
432
G = 
9231845
54
    (22)
, then subtract both sides of equation (22) from both sides of equation (7), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
-500D - 
3050
3
E - 
12455
9
F - 
86821
54
G = - 
57400
27
    (5)
-2160D -4320E -5820F -6720G = -8950    (6)
-6860D - 
40670
3
E - 
163205
9
F - 
1126015
54
G = - 
755314
27
    (7)

Multiply both sides of equation (4) by 125
Divide the two sides of equation (4) by 16, the equation can be obtained:
        -500D - 
3125
3
E - 
51875
36
F - 
730625
432
G = - 
244375
108
    (23)
, then subtract both sides of equation (23) from both sides of equation (5), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F + 
12019
144
G = 
4925
36
    (5)
-2160D -4320E -5820F -6720G = -8950    (6)
-6860D - 
40670
3
E - 
163205
9
F - 
1126015
54
G = - 
755314
27
    (7)

Multiply both sides of equation (4) by 135
Divide the two sides of equation (4) by 4, the equation can be obtained:
        -2160D -4500E -6225F - 
29225
4
G = -9775    (24)
, then subtract both sides of equation (24) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F + 
12019
144
G = 
4925
36
    (5)
 180E + 405F + 
2345
4
G = 825    (6)
-6860D - 
40670
3
E - 
163205
9
F - 
1126015
54
G = - 
755314
27
    (7)

Multiply both sides of equation (4) by 1715
Divide the two sides of equation (4) by 16, the equation can be obtained:
        -6860D - 
42875
3
E - 
711725
36
F - 
10024175
432
G = - 
3352825
108
    (25)
, then subtract both sides of equation (25) from both sides of equation (7), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F + 
12019
144
G = 
4925
36
    (5)
 180E + 405F + 
2345
4
G = 825    (6)
 735E + 
6545
4
F + 
112895
48
G = 
36841
12
    (7)

Multiply both sides of equation (5) by 36
Divide the two sides of equation (5) by 5, the equation can be obtained:
         180E + 411F + 
12019
20
G = 985    (26)
, then subtract both sides of equation (26) from both sides of equation (6), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F + 
12019
144
G = 
4925
36
    (5)
-6F - 
147
10
G = -160    (6)
 735E + 
6545
4
F + 
112895
48
G = 
36841
12
    (7)

Multiply both sides of equation (5) by 147
Divide the two sides of equation (5) by 5, the equation can be obtained:
         735E + 
6713
4
F + 
588931
240
G = 
48265
12
    (27)
, then subtract both sides of equation (27) from both sides of equation (7), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F + 
12019
144
G = 
4925
36
    (5)
-6F - 
147
10
G = -160    (6)
-42F - 
1019
10
G = -952    (7)

Multiply both sides of equation (6) by 7, the equation can be obtained:
        -42F - 
1029
10
G = -1120    (28)
, then subtract both sides of equation (28) from both sides of equation (7), the equations are reduced to:
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F + 
12019
144
G = 
4925
36
    (5)
-6F - 
147
10
G = -160    (6)
 G = 168    (7)

Multiply both sides of equation (7) by 147
Divide both sides of equation (7) by 10, get the equation：
         
147
10
G = 
12348
5
    (29)
, then add the two sides of equation (29) to both sides of equation (6), get the equation：
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F + 
12019
144
G = 
4925
36
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (7) by 12019
Divide both sides of equation (7) by 144, get the equation：
         
12019
144
G = 
84133
6
    (30)
, then subtract both sides of equation (30) from both sides of equation (5), get the equation：
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F - 
5845
27
G = - 
7820
27
    (4)
 25E + 
685
12
F = - 
499873
36
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (7) by 5845
Divide both sides of equation (7) by 27, get the equation：
         
5845
27
G = 
327320
9
    (31)
, then add the two sides of equation (31) to both sides of equation (4), get the equation：
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F + 
3661
16
G = 
769
2
    (3)
-64D - 
400
3
E - 
1660
9
F = 
974140
27
    (4)
 25E + 
685
12
F = - 
499873
36
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (7) by 3661
Divide both sides of equation (7) by 16, get the equation：
         
3661
16
G = 
76881
2
    (32)
, then subtract both sides of equation (32) from both sides of equation (3), get the equation：
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F -63G = -120    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F = -38056    (3)
-64D - 
400
3
E - 
1660
9
F = 
974140
27
    (4)
 25E + 
685
12
F = - 
499873
36
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (7) by 63, get the equation：
         63G = 10584    (33)
, then add the two sides of equation (33) to both sides of equation (2), get the equation：
 A + B + C + D + E + F + G = 2    (1)
-32B -48C -56D -60E -62F = 10464    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F = -38056    (3)
-64D - 
400
3
E - 
1660
9
F = 
974140
27
    (4)
 25E + 
685
12
F = - 
499873
36
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Subtract both sides of equation (7) from both sides of equation (1), get the equation：
 A + B + C + D + E + F = -166    (1)
-32B -48C -56D -60E -62F = 10464    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F = -38056    (3)
-64D - 
400
3
E - 
1660
9
F = 
974140
27
    (4)
 25E + 
685
12
F = - 
499873
36
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (6) by 685
Divide both sides of equation (6) by 72, get the equation：
        - 
685
12
F = 
395519
18
    (34)
, then add the two sides of equation (34) to both sides of equation (5), get the equation：
 A + B + C + D + E + F = -166    (1)
-32B -48C -56D -60E -62F = 10464    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F = -38056    (3)
-64D - 
400
3
E - 
1660
9
F = 
974140
27
    (4)
 25E = 
97055
12
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (6) by 830
Divide both sides of equation (6) by 27, get the equation：
        - 
1660
9
F = 
1916968
27
    (35)
, then subtract both sides of equation (35) from both sides of equation (4), get the equation：
 A + B + C + D + E + F = -166    (1)
-32B -48C -56D -60E -62F = 10464    (2)
 81C + 
297
2
D + 
765
4
E + 
1725
8
F = -38056    (3)
-64D - 
400
3
E = - 
314276
9
    (4)
 25E = 
97055
12
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (6) by 575
Divide both sides of equation (6) by 16, get the equation：
        - 
1725
8
F = 
332005
4
    (36)
, then add the two sides of equation (36) to both sides of equation (3), get the equation：
 A + B + C + D + E + F = -166    (1)
-32B -48C -56D -60E -62F = 10464    (2)
 81C + 
297
2
D + 
765
4
E = 
179781
4
    (3)
-64D - 
400
3
E = - 
314276
9
    (4)
 25E = 
97055
12
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (6) by 31
Divide both sides of equation (6) by 3, get the equation：
        -62F = 
357988
15
    (37)
, then subtract both sides of equation (37) from both sides of equation (2), get the equation：
 A + B + C + D + E + F = -166    (1)
-32B -48C -56D -60E = - 
201028
15
    (2)
 81C + 
297
2
D + 
765
4
E = 
179781
4
    (3)
-64D - 
400
3
E = - 
314276
9
    (4)
 25E = 
97055
12
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Divide both sides of equation (6) by 6, get the equation：
        -1F = 
5774
15
    (38)
, then add the two sides of equation (38) to both sides of equation (1), get the equation：
 A + B + C + D + E = 
3284
15
    (1)
-32B -48C -56D -60E = - 
201028
15
    (2)
 81C + 
297
2
D + 
765
4
E = 
179781
4
    (3)
-64D - 
400
3
E = - 
314276
9
    (4)
 25E = 
97055
12
    (5)
-6F = 
11548
5
    (6)
 G = 168    (7)

Multiply both sides of equation (5) by 16
Divide both sides of equation (5) by 3, get the equation：
         
400
3
E = 
388220
9
    (39)
, then add the two sides of equation (39) to both sides of equation (4), get the equation：
 A + B + C + D + E = 
3284
15
    (1)
-32B -48C -56D -60E = - 
201028
15
    (2)
 81C + 
297
2
D + 
765
4
E = 
179781
4
    (3)
-64D = 8216    (4)
 25E = 
97055
12
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Multiply both sides of equation (5) by 153
Divide both sides of equation (5) by 20, get the equation：
         
765
4
E = 
989961
16
    (40)
, then subtract both sides of equation (40) from both sides of equation (3), get the equation：
 A + B + C + D + E = 
3284
15
    (1)
-32B -48C -56D -60E = - 
201028
15
    (2)
 81C + 
297
2
D = - 
270837
16
    (3)
-64D = 8216    (4)
 25E = 
97055
12
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Multiply both sides of equation (5) by 12
Divide both sides of equation (5) by 5, get the equation：
         60E = 19411    (41)
, then add the two sides of equation (41) to both sides of equation (2), get the equation：
 A + B + C + D + E = 
3284
15
    (1)
-32B -48C -56D = 
90137
15
    (2)
 81C + 
297
2
D = - 
270837
16
    (3)
-64D = 8216    (4)
 25E = 
97055
12
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Divide both sides of equation (5) by 25, get the equation：
         E = 
19411
60
    (42)
, then subtract both sides of equation (42) from both sides of equation (1), get the equation：
 A + B + C + D = - 
1255
12
    (1)
-32B -48C -56D = 
90137
15
    (2)
 81C + 
297
2
D = - 
270837
16
    (3)
-64D = 8216    (4)
 25E = 
97055
12
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Multiply both sides of equation (4) by 297
Divide both sides of equation (4) by 128, get the equation：
        - 
297
2
D = 
305019
16
    (43)
, then add the two sides of equation (43) to both sides of equation (3), get the equation：
 A + B + C + D = - 
1255
12
    (1)
-32B -48C -56D = 
90137
15
    (2)
 81C = 
17091
8
    (3)
-64D = 8216    (4)
 E = 
19411
60
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Multiply both sides of equation (4) by 7
Divide both sides of equation (4) by 8, get the equation：
        -56D = 7189    (44)
, then subtract both sides of equation (44) from both sides of equation (2), get the equation：
 A + B + C + D = - 
1255
12
    (1)
-32B -48C = - 
17698
15
    (2)
 81C = 
17091
8
    (3)
-64D = 8216    (4)
 E = 
19411
60
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Divide both sides of equation (4) by 64, get the equation：
        -1D = 
1027
8
    (45)
, then add the two sides of equation (45) to both sides of equation (1), get the equation：
 A + B + C = 
571
24
    (1)
-32B -48C = - 
17698
15
    (2)
 81C = 
17091
8
    (3)
-64D = 8216    (4)
 E = 
19411
60
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Multiply both sides of equation (3) by 16
Divide both sides of equation (3) by 27, get the equation：
         48C = 1266    (46)
, then add the two sides of equation (46) to both sides of equation (2), get the equation：
 A + B + C = 
571
24
    (1)
-32B = 
1292
15
    (2)
 81C = 
17091
8
    (3)
 D = - 
1027
8
    (4)
 E = 
19411
60
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Divide both sides of equation (3) by 81, get the equation：
         C = 
211
8
    (47)
, then subtract both sides of equation (47) from both sides of equation (1), get the equation：
 A + B = - 
31
12
    (1)
-32B = 
1292
15
    (2)
 81C = 
17091
8
    (3)
 D = - 
1027
8
    (4)
 E = 
19411
60
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

Divide both sides of equation (2) by 32, get the equation：
        -1B = 
323
120
    (48)
, then add the two sides of equation (48) to both sides of equation (1), get the equation：
 A = 
13
120
    (1)
-32B = 
1292
15
    (2)
 C = 
211
8
    (3)
 D = - 
1027
8
    (4)
 E = 
19411
60
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
13
120
    (1)
 B = - 
323
120
    (2)
 C = 
211
8
    (3)
 D = - 
1027
8
    (4)
 E = 
19411
60
    (5)
 F = - 
5774
15
    (6)
 G = 168    (7)


Therefore, the solution of the equation set is:
A = 
13
120
B = - 
323
120
C = 
211
8
D = - 
1027
8
E = 
19411
60
F = - 
5774
15
G = 168


Convert the solution of the equation set to decimals:
A = 0.108333
B = -2.691667
C = 26.375000
D = -128.375000
E = 323.516667
F = -384.933333
G = 168

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。