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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 = 40    (1)
 3A + 4B -1C = 0    (2)
 3A + 6B -1D = 0    (3)
 C + 2D + 4E = 20    (4)
 C + 4D + 12E -1F = 0    (5)
 D + 6E -1G = 0    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)
Question solving process:

Multiply both sides of equation (1) by 3, the equation can be obtained:
         3A + 3B = 120    (10)
, then subtract both sides of equation (10) from both sides of equation (2), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3A + 6B -1D = 0    (3)
 C + 2D + 4E = 20    (4)
 C + 4D + 12E -1F = 0    (5)
 D + 6E -1G = 0    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (1) by 3, the equation can be obtained:
         3A + 3B = 120    (11)
, then subtract both sides of equation (11) from both sides of equation (3), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3B -1D = -120    (3)
 C + 2D + 4E = 20    (4)
 C + 4D + 12E -1F = 0    (5)
 D + 6E -1G = 0    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (2) by 3, the equation can be obtained:
         3B -3C = -360    (12)
, then subtract both sides of equation (12) from both sides of equation (3), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 C + 2D + 4E = 20    (4)
 C + 4D + 12E -1F = 0    (5)
 D + 6E -1G = 0    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Divide the two sides of equation (3) by 3, the equation can be obtained:
         C - 
1
3
D = 80    (13)
, then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 C + 4D + 12E -1F = 0    (5)
 D + 6E -1G = 0    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Divide the two sides of equation (3) by 3, the equation can be obtained:
         C - 
1
3
D = 80    (14)
, then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
13
3
D + 12E -1F = -80    (5)
 D + 6E -1G = 0    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (4) by 13
Divide the two sides of equation (4) by 7, the equation can be obtained:
         
13
3
D + 
52
7
E = - 
780
7
    (15)
, then subtract both sides of equation (15) from both sides of equation (5), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 D + 6E -1G = 0    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (4) by 3
Divide the two sides of equation (4) by 7, the equation can be obtained:
         D + 
12
7
E = - 
180
7
    (16)
, then subtract both sides of equation (16) from both sides of equation (6), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
30
7
E -1G = 
180
7
    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (5) by 15
Divide the two sides of equation (5) by 16, the equation can be obtained:
         
30
7
E - 
15
16
F = 
825
28
    (17)
, then subtract both sides of equation (17) from both sides of equation (6), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 F + G + H + I = -60    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (6) by 16
Divide the two sides of equation (6) by 15, the equation can be obtained:
         F - 
16
15
G = -4    (18)
, then subtract both sides of equation (18) from both sides of equation (7), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G + H + I = -56    (7)
 F + 2G + 3H + 4I = 0    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (6) by 16
Divide the two sides of equation (6) by 15, the equation can be obtained:
         F - 
16
15
G = -4    (19)
, then subtract both sides of equation (19) from both sides of equation (8), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G + H + I = -56    (7)
 
46
15
G + 3H + 4I = 4    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (7) by 46
Divide the two sides of equation (7) by 31, the equation can be obtained:
         
46
15
G + 
46
31
H + 
46
31
I = - 
2576
31
    (20)
, then subtract both sides of equation (20) from both sides of equation (8), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G + H + I = -56    (7)
 
47
31
H + 
78
31
I = 
2700
31
    (8)
 G + 3H + 6I = 0    (9)

Multiply both sides of equation (7) by 15
Divide the two sides of equation (7) by 31, the equation can be obtained:
         G + 
15
31
H + 
15
31
I = - 
840
31
    (21)
, then subtract both sides of equation (21) from both sides of equation (9), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G + H + I = -56    (7)
 
47
31
H + 
78
31
I = 
2700
31
    (8)
 
78
31
H + 
171
31
I = 
840
31
    (9)

Multiply both sides of equation (8) by 78
Divide the two sides of equation (8) by 47, the equation can be obtained:
         
78
31
H + 
6084
1457
I = 
210600
1457
    (22)
, then subtract both sides of equation (22) from both sides of equation (9), the equations are reduced to:
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G + H + I = -56    (7)
 
47
31
H + 
78
31
I = 
2700
31
    (8)
 
63
47
I = - 
5520
47
    (9)

Multiply both sides of equation (9) by 1222
Divide both sides of equation (9) by 651, get the equation：
         
78
31
I = - 
47840
217
    (23)
, then subtract both sides of equation (23) from both sides of equation (8), get the equation：
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G + H + I = -56    (7)
 
47
31
H = 
66740
217
    (8)
 
63
47
I = - 
5520
47
    (9)

Multiply both sides of equation (9) by 47
Divide both sides of equation (9) by 63, get the equation：
         I = - 
1840
21
    (24)
, then subtract both sides of equation (24) from both sides of equation (7), get the equation：
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G + H = 
664
21
    (7)
 
47
31
H = 
66740
217
    (8)
 
63
47
I = - 
5520
47
    (9)

Multiply both sides of equation (8) by 31
Divide both sides of equation (8) by 47, get the equation：
         H = 
1420
7
    (25)
, then subtract both sides of equation (25) from both sides of equation (7), get the equation：
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F -1G = - 
15
4
    (6)
 
31
15
G = - 
3596
21
    (7)
 
47
31
H = 
66740
217
    (8)
 I = - 
1840
21
    (9)

Multiply both sides of equation (7) by 15
Divide both sides of equation (7) by 31, get the equation：
         G = - 
580
7
    (26)
, then add the two sides of equation (26) to both sides of equation (6), get the equation：
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E -1F = 
220
7
    (5)
 
15
16
F = - 
2425
28
    (6)
 
31
15
G = - 
3596
21
    (7)
 H = 
1420
7
    (8)
 I = - 
1840
21
    (9)

Multiply both sides of equation (6) by 16
Divide both sides of equation (6) by 15, get the equation：
         F = - 
1940
21
    (27)
, then add the two sides of equation (27) to both sides of equation (5), get the equation：
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D + 4E = -60    (4)
 
32
7
E = - 
1280
21
    (5)
 
15
16
F = - 
2425
28
    (6)
 G = - 
580
7
    (7)
 H = 
1420
7
    (8)
 I = - 
1840
21
    (9)

Multiply both sides of equation (5) by 7
Divide both sides of equation (5) by 8, get the equation：
         4E = - 
160
3
    (28)
, then subtract both sides of equation (28) from both sides of equation (4), get the equation：
 A + B = 40    (1)
 B -1C = -120    (2)
 3C -1D = 240    (3)
 
7
3
D = - 
20
3
    (4)
 
32
7
E = - 
1280
21
    (5)
 F = - 
1940
21
    (6)
 G = - 
580
7
    (7)
 H = 
1420
7
    (8)
 I = - 
1840
21
    (9)

Multiply both sides of equation (4) by 3
Divide both sides of equation (4) by 7, get the equation：
         D = - 
20
7
    (29)
, then add the two sides of equation (29) to both sides of equation (3), get the equation：
 A + B = 40    (1)
 B -1C = -120    (2)
 3C = 
1660
7
    (3)
 
7
3
D = - 
20
3
    (4)
 E = - 
40
3
    (5)
 F = - 
1940
21
    (6)
 G = - 
580
7
    (7)
 H = 
1420
7
    (8)
 I = - 
1840
21
    (9)

Divide both sides of equation (3) by 3, get the equation：
         C = 
1660
21
    (30)
, then add the two sides of equation (30) to both sides of equation (2), get the equation：
 A + B = 40    (1)
 B = - 
860
21
    (2)
 3C = 
1660
7
    (3)
 D = - 
20
7
    (4)
 E = - 
40
3
    (5)
 F = - 
1940
21
    (6)
 G = - 
580
7
    (7)
 H = 
1420
7
    (8)
 I = - 
1840
21
    (9)

Subtract both sides of equation (2) from both sides of equation (1), get the equation：
 A = 
1700
21
    (1)
 B = - 
860
21
    (2)
 C = 
1660
21
    (3)
 D = - 
20
7
    (4)
 E = - 
40
3
    (5)
 F = - 
1940
21
    (6)
 G = - 
580
7
    (7)
 H = 
1420
7
    (8)
 I = - 
1840
21
    (9)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
1700
21
    (1)
 B = - 
860
21
    (2)
 C = 
1660
21
    (3)
 D = - 
20
7
    (4)
 E = - 
40
3
    (5)
 F = - 
1940
21
    (6)
 G = - 
580
7
    (7)
 H = 
1420
7
    (8)
 I = - 
1840
21
    (9)


Therefore, the solution of the equation set is:
A = 
1700
21
B = - 
860
21
C = 
1660
21
D = - 
20
7
E = - 
40
3
F = - 
1940
21
G = - 
580
7
H = 
1420
7
I = - 
1840
21


Convert the solution of the equation set to decimals:
A = 80.952381
B = -40.952381
C = 79.047619
D = -2.857143
E = -13.333333
F = -92.380952
G = -82.857143
H = 202.857143
I = -87.619048

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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