27A + 81B = 40 2C + 4D + 8E = 35 27A + 108B - C = 0 9A + 54B - D = 0 3F + 9G + 27H + 81I = -20 F + 6G + 27H + 108I = 0 G + 9H + 54I = 0 C + 4D + 12E - F = 0 D + 6E

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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:

(1)

(2)

108

-1

(3)

-1

(4)

-20

(5)

108

(6)

(7)

-1

(8)

-1

(9)

Question solving process:

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:

(1)

(2)

-1

-40

(3)

-1

(4)

-20

(5)

108

(6)

(7)

-1

(8)

-1

(9)

Divide the two sides of equation (1) by 3, the equation can be obtained:

(10)

, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:

(1)

(2)

-1

-40

(3)

-1

(4)

-20

(5)

108

(6)

(7)

-1

(8)

-1

(9)

交After the exchange of equation (2) and equation (3)， the equation system becomes:

(1)

-1

-40

(2)

(3)

-1

(4)

-20

(5)

108

(6)

(7)

-1

(8)

-1

(9)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:

(1)

-1

-40

(2)

(3)

-1

(4)

-20

(5)

108

(6)

(7)

-1

(8)

-1

(9)

Divide the two sides of equation (3) by 2, the equation can be obtained:

(11)

, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-20

(5)

108

(6)

(7)

-1

(8)

-1

(9)

Divide the two sides of equation (3) by 2, the equation can be obtained:

(12)

, then subtract both sides of equation (12) from both sides of equation (8), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-20

(5)

108

(6)

(7)

-1

(8)

-1

(9)

Multiply both sides of equation (4) by 2
Divide the two sides of equation (4) by 3, the equation can be obtained:

-2

(13)

, then add the two sides of equation (13) to both sides of equation (8), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-20

(5)

108

(6)

(7)

-1

205

(8)

-1

(9)

Divide the two sides of equation (4) by 3, the equation can be obtained:

-1

(14)

, then add the two sides of equation (14) to both sides of equation (9), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-20

(5)

108

(6)

(7)

-1

205

(8)

-1

(9)

交After the exchange of equation (5) and equation (8)， the equation system becomes:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

-20

(8)

-1

(9)

Multiply both sides of equation (5) by 7
Divide the two sides of equation (5) by 8, the equation can be obtained:

1435

144

(15)

, then subtract both sides of equation (15) from both sides of equation (9), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

-20

(8)

-1

625

(9)

Multiply both sides of equation (6) by 3, the equation can be obtained:

324

(16)

, then subtract both sides of equation (16) from both sides of equation (8), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

-9

-54

-243

-20

(8)

-1

625

(9)

Multiply both sides of equation (6) by 7
Divide the two sides of equation (6) by 8, the equation can be obtained:

189

(17)

, then subtract both sides of equation (17) from both sides of equation (9), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

-9

-54

-243

-20

(8)

189

625

(9)

Multiply both sides of equation (7) by 9, the equation can be obtained:

486

(18)

, then add the two sides of equation (18) to both sides of equation (8), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

243

-20

(8)

189

625

(9)

Multiply both sides of equation (7) by 25
Divide the two sides of equation (7) by 4, the equation can be obtained:

225

675

(19)

, then add the two sides of equation (19) to both sides of equation (9), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

243

-20

(8)

261

243

625

(9)

Multiply both sides of equation (8) by 29
Divide the two sides of equation (8) by 24, the equation can be obtained:

261

2349

145

(20)

, then subtract both sides of equation (20) from both sides of equation (9), the equations are reduced to:

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

243

-20

(8)

405

595

(9)

Multiply both sides of equation (9) by 24
Divide both sides of equation (9) by 5, get the equation：

-243

357

(21)

, then add the two sides of equation (21) to both sides of equation (8), get the equation：

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

(7)

317

(8)

405

595

(9)

Multiply both sides of equation (9) by 16
Divide both sides of equation (9) by 15, get the equation：

-54

119

(22)

, then add the two sides of equation (22) to both sides of equation (7), get the equation：

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

108

(6)

119

(7)

317

(8)

405

595

(9)

Multiply both sides of equation (9) by 32
Divide both sides of equation (9) by 15, get the equation：

-108

238

(23)

, then add the two sides of equation (23) to both sides of equation (6), get the equation：

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

238

(6)

119

(7)

317

(8)

405

595

(9)

Divide both sides of equation (8) by 3, get the equation：

317

(24)

, then subtract both sides of equation (24) from both sides of equation (7), get the equation：

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

238

(6)

(7)

317

(8)

119

162

(9)

Subtract both sides of equation (8) from both sides of equation (6), get the equation：

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

475

(6)

(7)

317

(8)

119

162

(9)

Multiply both sides of equation (7) by 6, get the equation：

-79

(25)

, then subtract both sides of equation (25) from both sides of equation (6), get the equation：

(1)

-1

-40

(2)

(3)

-3

-4

(4)

-1

205

(5)

(6)

(7)

317

(8)

119

162

(9)

Add both sides of equation (6) to both sides of equation (5), get the equation：

(1)

-1

-40

(2)

(3)

-3

-4

(4)

104

(5)

(6)

(7)

317

(8)

119

162

(9)

Multiply both sides of equation (5) by 3
Divide both sides of equation (5) by 4, get the equation：

(26)

, then add the two sides of equation (26) to both sides of equation (4), get the equation：

(1)

-1

-40

(2)

(3)

-3

(4)

104

(5)

(6)

(7)

317

(8)

119

162

(9)

Multiply both sides of equation (5) by 3
Divide both sides of equation (5) by 2, get the equation：

(27)

, then subtract both sides of equation (27) from both sides of equation (3), get the equation：

(1)

-1

-40

(2)

157

(3)

-3

(4)

104

(5)

(6)

(7)

317

(8)

119

162

(9)

Multiply both sides of equation (4) by 4
Divide both sides of equation (4) by 3, get the equation：

-4

(28)

, then add the two sides of equation (28) to both sides of equation (3), get the equation：

(1)

-1

-40

(2)

(3)

-3

(4)

(5)

(6)

(7)

317

(8)

119

162

(9)

Divide both sides of equation (3) by 2, get the equation：

(29)

, then add the two sides of equation (29) to both sides of equation (2), get the equation：

(1)

(2)

(3)

(4)

(5)

(6)

(7)

317

(8)

119

162

(9)

Multiply both sides of equation (2) by 3, get the equation：

(30)

, then subtract both sides of equation (30) from both sides of equation (1), get the equation：

161

(1)

(2)

(3)

(4)

(5)

(6)

(7)

317

(8)

119

162

(9)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：

161

(1)

(2)

(3)

(4)

(5)

(6)

(7)

317

(8)

119

162

(9)

Therefore, the solution of the equation set is:

A =

161

B =

C =

D =

E =

F =

G =

H =

317

I =

119

162

Convert the solution of the equation set to decimals:

A =

2.981481

B =

-0.500000

C =

26.500000

D =

-0.166667

E =

-2.166667

F =

-0.166667

G =

-13.166667

H =

5.870370

I =

-0.734568

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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