Mathematics
         
语言：中文    Language:English
Equations   
Fold
Unary equation
Multivariate equation
Math OP  
Unfold
Linear algebra      
Unfold
Derivative function
Function image
Hot issues
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:
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
 12A + 8B + C + 2D + 3E + F = 
6151
10
    (2)
 10A + 5B + C + 2D + 3E + 2F = 
2507
4
    (3)
 10A + 5B + C + 2E + F = 
2507
5
    (4)
 E = 25    (5)
 F = 12    (6)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
-1C -1D -1E -1F = - 
2507
10
    (2)
 10A + 5B + C + 2D + 3E + 2F = 
2507
4
    (3)
 10A + 5B + C + 2E + F = 
2507
5
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 6, the equation can be obtained:
         10A + 
20
3
B + 
5
3
C + 
5
2
D + 
10
3
E + 
5
3
F = 
1443
2
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
-1C -1D -1E -1F = - 
2507
10
    (2)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (3)
 10A + 5B + C + 2E + F = 
2507
5
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 6, the equation can be obtained:
         10A + 
20
3
B + 
5
3
C + 
5
2
D + 
10
3
E + 
5
3
F = 
1443
2
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
-1C -1D -1E -1F = - 
2507
10
    (2)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (3)
- 
5
3
B - 
2
3
C - 
5
2
D - 
4
3
E - 
2
3
F = - 
2201
10
    (4)
 E = 25    (5)
 F = 12    (6)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (2)
-1C -1D -1E -1F = - 
2507
10
    (3)
- 
5
3
B - 
2
3
C - 
5
2
D - 
4
3
E - 
2
3
F = - 
2201
10
    (4)
 E = 25    (5)
 F = 12    (6)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (2)
-1C -1D -1E -1F = - 
2507
10
    (3)
-2D -1E -1F = - 
2507
20
    (4)
 E = 25    (5)
 F = 12    (6)

Add both sides of equation (6) to both sides of equation (4), get the equation：
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (2)
-1C -1D -1E -1F = - 
2507
10
    (3)
-2D -1E = - 
2267
20
    (4)
 E = 25    (5)
 F = 12    (6)

Add both sides of equation (6) to both sides of equation (3), get the equation：
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E + 
1
3
F = - 
379
4
    (2)
-1C -1D -1E = - 
2387
10
    (3)
-2D -1E = - 
2267
20
    (4)
 E = 25    (5)
 F = 12    (6)

Divide both sides of equation (6) by 3, get the equation：
         
1
3
F = 4    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation：
 12A + 8B + 2C + 3D + 4E + 2F = 
4329
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (2)
-1C -1D -1E = - 
2387
10
    (3)
-2D -1E = - 
2267
20
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (6) by 2, get the equation：
         2F = 24    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation：
 12A + 8B + 2C + 3D + 4E = 
4209
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (2)
-1C -1D -1E = - 
2387
10
    (3)
-2D -1E = - 
2267
20
    (4)
 E = 25    (5)
 F = 12    (6)

Add both sides of equation (5) to both sides of equation (4), get the equation：
 12A + 8B + 2C + 3D + 4E = 
4209
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (2)
-1C -1D -1E = - 
2387
10
    (3)
-2D = - 
1767
20
    (4)
 E = 25    (5)
 F = 12    (6)

Add both sides of equation (5) to both sides of equation (3), get the equation：
 12A + 8B + 2C + 3D + 4E = 
4209
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D - 
1
3
E = - 
395
4
    (2)
-1C -1D = - 
2137
10
    (3)
-2D = - 
1767
20
    (4)
 E = 25    (5)
 F = 12    (6)

Divide both sides of equation (5) by 3, get the equation：
         
1
3
E = 
25
3
    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 12A + 8B + 2C + 3D + 4E = 
4209
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D = - 
1085
12
    (2)
-1C -1D = - 
2137
10
    (3)
-2D = - 
1767
20
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (5) by 4, get the equation：
         4E = 100    (12)
, then subtract both sides of equation (12) from both sides of equation (1), get the equation：
 12A + 8B + 2C + 3D = 
3709
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D = - 
1085
12
    (2)
-1C -1D = - 
2137
10
    (3)
-2D = - 
1767
20
    (4)
 E = 25    (5)
 F = 12    (6)

Divide both sides of equation (4) by 2, get the equation：
        -1D = - 
1767
40
    (13)
, then subtract both sides of equation (13) from both sides of equation (3), get the equation：
 12A + 8B + 2C + 3D = 
3709
5
    (1)
- 
5
3
B - 
2
3
C - 
1
2
D = - 
1085
12
    (2)
-1C = - 
6781
40
    (3)
-2D = - 
1767
20
    (4)
 E = 25    (5)
 F = 12    (6)

Divide both sides of equation (4) by 4, get the equation：
        - 
1
2
D = - 
1767
80
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 12A + 8B + 2C + 3D = 
3709
5
    (1)
- 
5
3
B - 
2
3
C = - 
16399
240
    (2)
-1C = - 
6781
40
    (3)
-2D = - 
1767
20
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (4) by 3
Divide both sides of equation (4) by 2, get the equation：
        -3D = - 
5301
40
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 12A + 8B + 2C = 
24371
40
    (1)
- 
5
3
B - 
2
3
C = - 
16399
240
    (2)
-1C = - 
6781
40
    (3)
-2D = - 
1767
20
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 3, get the equation：
        - 
2
3
C = - 
6781
60
    (16)
, then subtract both sides of equation (16) from both sides of equation (2), get the equation：
 12A + 8B + 2C = 
24371
40
    (1)
- 
5
3
B = 
715
16
    (2)
-1C = - 
6781
40
    (3)
 D = 
1767
40
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (3) by 2, get the equation：
        -2C = - 
6781
20
    (17)
, then add the two sides of equation (17) to both sides of equation (1), get the equation：
 12A + 8B = 
10809
40
    (1)
- 
5
3
B = 
715
16
    (2)
-1C = - 
6781
40
    (3)
 D = 
1767
40
    (4)
 E = 25    (5)
 F = 12    (6)

Multiply both sides of equation (2) by 24
Divide both sides of equation (2) by 5, get the equation：
        -8B = 
429
2
    (18)
, then add the two sides of equation (18) to both sides of equation (1), get the equation：
 12A = 
19389
40
    (1)
- 
5
3
B = 
715
16
    (2)
 C = 
6781
40
    (3)
 D = 
1767
40
    (4)
 E = 25    (5)
 F = 12    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
6463
160
    (1)
 B = - 
429
16
    (2)
 C = 
6781
40
    (3)
 D = 
1767
40
    (4)
 E = 25    (5)
 F = 12    (6)


Therefore, the solution of the equation set is:
A = 
6463
160
B = - 
429
16
C = 
6781
40
D = 
1767
40
E = 25
F = 12


Convert the solution of the equation set to decimals:
A = 40.393750
B = -26.812500
C = 169.525000
D = 44.175000
E = 25
F = 12

解方程组的详细方法请参阅：《多元一次方程组的解法》
return







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