Mathematics
         
语言:中文    Language:English
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:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
 6A + 6B + C + 2D + 3E + F = 
6151
10
    (2)
 4A + 6B + C + 2D + 3E + 2F = 
2507
4
    (3)
 4A + 4B + C + 2E + F = 
2507
5
    (4)
 E = 25    (5)
 A = 12    (6)
Question solving process:

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

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 3, the equation can be obtained:
         4A + 4B + 
4
3
C + 
4
3
D + 
8
3
E + 
4
3
F = 
2886
5
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
-1C -1E -1F = 
2507
10
    (2)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (3)
 4A + 4B + C + 2E + F = 
2507
5
    (4)
 E = 25    (5)
 A = 12    (6)

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 3, the equation can be obtained:
         4A + 4B + 
4
3
C + 
4
3
D + 
8
3
E + 
4
3
F = 
2886
5
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
-1C -1E -1F = 
2507
10
    (2)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (3)
1
3
C 
4
3
D 
2
3
E 
1
3
F = 
379
5
    (4)
 E = 25    (5)
 A = 12    (6)

Divide the two sides of equation (1) by 6, the equation can be obtained:
         A + B + 
1
3
C + 
1
3
D + 
2
3
E + 
1
3
F = 
1443
10
    (9)
, then subtract both sides of equation (9) from both sides of equation (6), the equations are reduced to:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
-1C -1E -1F = 
2507
10
    (2)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (3)
1
3
C 
4
3
D 
2
3
E 
1
3
F = 
379
5
    (4)
 E = 25    (5)
-1B 
1
3
C 
1
3
D 
2
3
E 
1
3
F = 
1323
10
    (6)

交After the exchange of equation (2) and equation (3), the equation system becomes:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (2)
-1C -1E -1F = 
2507
10
    (3)
1
3
C 
4
3
D 
2
3
E 
1
3
F = 
379
5
    (4)
 E = 25    (5)
-1B 
1
3
C 
1
3
D 
2
3
E 
1
3
F = 
1323
10
    (6)

Divide the two sides of equation (2) by 2, the equation can be obtained:
         B 
1
6
C + 
1
3
D + 
1
6
E + 
1
3
F = 
991
40
    (10)
, then add the two sides of equation (10) to both sides of equation (6), the equations are reduced to:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (2)
-1C -1E -1F = 
2507
10
    (3)
1
3
C 
4
3
D 
2
3
E 
1
3
F = 
379
5
    (4)
 E = 25    (5)
1
2
C 
1
2
E = 
4301
40
    (6)

Divide the two sides of equation (3) by 3, the equation can be obtained:
        
1
3
C 
1
3
E 
1
3
F = 
2507
30
    (11)
, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (2)
-1C -1E -1F = 
2507
10
    (3)
4
3
D 
1
3
E = 
233
30
    (4)
 E = 25    (5)
1
2
C 
1
2
E = 
4301
40
    (6)

Divide the two sides of equation (3) by 2, the equation can be obtained:
        
1
2
C 
1
2
E 
1
2
F = 
2507
20
    (12)
, then subtract both sides of equation (12) from both sides of equation (6), the equations are reduced to:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (2)
-1C -1E -1F = 
2507
10
    (3)
4
3
D 
1
3
E = 
233
30
    (4)
 E = 25    (5)
 
1
2
F = 
713
40
    (6)

Multiply both sides of equation (6) by 2, get the equation:
         F = 
713
20
    (13)
, then add the two sides of equation (13) to both sides of equation (3), get the equation:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E + 
2
3
F = 
991
20
    (2)
-1C -1E = 
4301
20
    (3)
4
3
D 
1
3
E = 
233
30
    (4)
 E = 25    (5)
 
1
2
F = 
713
40
    (6)

Multiply both sides of equation (6) by 4
Divide both sides of equation (6) by 3, get the equation:
         
2
3
F = 
713
30
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation:
 6A + 6B + 2C + 2D + 4E + 2F = 
4329
5
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E = 
1547
60
    (2)
-1C -1E = 
4301
20
    (3)
4
3
D 
1
3
E = 
233
30
    (4)
 E = 25    (5)
 
1
2
F = 
713
40
    (6)

Multiply both sides of equation (6) by 4, get the equation:
         2F = 
713
10
    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
 6A + 6B + 2C + 2D + 4E = 
1589
2
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E = 
1547
60
    (2)
-1C -1E = 
4301
20
    (3)
4
3
D 
1
3
E = 
233
30
    (4)
 E = 25    (5)
 
1
2
F = 
713
40
    (6)

Divide both sides of equation (5) by 3, get the equation:
         
1
3
E = 
25
3
    (16)
, then add the two sides of equation (16) to both sides of equation (4), get the equation:
 6A + 6B + 2C + 2D + 4E = 
1589
2
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E = 
1547
60
    (2)
-1C -1E = 
4301
20
    (3)
4
3
D = 
161
10
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Add both sides of equation (5) to both sides of equation (3), get the equation:
 6A + 6B + 2C + 2D + 4E = 
1589
2
    (1)
 2B 
1
3
C + 
2
3
D + 
1
3
E = 
1547
60
    (2)
-1C = 
3801
20
    (3)
4
3
D = 
161
10
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Divide both sides of equation (5) by 3, get the equation:
         
1
3
E = 
25
3
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation:
 6A + 6B + 2C + 2D + 4E = 
1589
2
    (1)
 2B 
1
3
C + 
2
3
D = 
349
20
    (2)
-1C = 
3801
20
    (3)
4
3
D = 
161
10
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Multiply both sides of equation (5) by 4, get the equation:
         4E = 100    (18)
, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
 6A + 6B + 2C + 2D = 
1389
2
    (1)
 2B 
1
3
C + 
2
3
D = 
349
20
    (2)
-1C = 
3801
20
    (3)
4
3
D = 
161
10
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Divide both sides of equation (4) by 2, get the equation:
        
2
3
D = 
161
20
    (19)
, then add the two sides of equation (19) to both sides of equation (2), get the equation:
 6A + 6B + 2C + 2D = 
1389
2
    (1)
 2B 
1
3
C = 
51
2
    (2)
-1C = 
3801
20
    (3)
4
3
D = 
161
10
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Multiply both sides of equation (4) by 3
Divide both sides of equation (4) by 2, get the equation:
        -2D = 
483
20
    (20)
, then add the two sides of equation (20) to both sides of equation (1), get the equation:
 6A + 6B + 2C = 
14373
20
    (1)
 2B 
1
3
C = 
51
2
    (2)
-1C = 
3801
20
    (3)
4
3
D = 
161
10
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Divide both sides of equation (3) by 3, get the equation:
        
1
3
C = 
1267
20
    (21)
, then subtract both sides of equation (21) from both sides of equation (2), get the equation:
 6A + 6B + 2C = 
14373
20
    (1)
 2B = 
1777
20
    (2)
-1C = 
3801
20
    (3)
 D = 
483
40
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Multiply both sides of equation (3) by 2, get the equation:
        -2C = 
3801
10
    (22)
, then add the two sides of equation (22) to both sides of equation (1), get the equation:
 6A + 6B = 
6771
20
    (1)
 2B = 
1777
20
    (2)
-1C = 
3801
20
    (3)
 D = 
483
40
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

Multiply both sides of equation (2) by 3, get the equation:
         6B = 
5331
20
    (23)
, then subtract both sides of equation (23) from both sides of equation (1), get the equation:
 6A = 72    (1)
 2B = 
1777
20
    (2)
 C = 
3801
20
    (3)
 D = 
483
40
    (4)
 E = 25    (5)
 F = 
713
20
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 12    (1)
 B = 
1777
40
    (2)
 C = 
3801
20
    (3)
 D = 
483
40
    (4)
 E = 25    (5)
 F = 
713
20
    (6)


Therefore, the solution of the equation set is:
A = 12
B = 
1777
40
C = 
3801
20
D = 
483
40
E = 25
F = 
713
20


Convert the solution of the equation set to decimals:
A = 12
B = 44.425000
C = 190.050000
D = -12.075000
E = 25
F = 35.650000

解方程组的详细方法请参阅:《多元一次方程组的解法》







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