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:
 A + B = 1679    (1)
 C + D = 118    (2)
 
21
5000
A + E = 10    (3)
 
13
125
A + F = 408    (4)
 
138
125
A + C = 227    (5)
- 
138
125
A + B -1C = 2030    (6)
Question solving process:

Multiply both sides of equation (1) by 21
Divide the two sides of equation (1) by 5000, the equation can be obtained:
         
21
5000
A + 
21
5000
B = 
35259
5000
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 A + B = 1679    (1)
 C + D = 118    (2)
- 
21
5000
B + E = 
14741
5000
    (3)
 
13
125
A + F = 408    (4)
 
138
125
A + C = 227    (5)
- 
138
125
A + B -1C = 2030    (6)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 125, the equation can be obtained:
         
13
125
A + 
13
125
B = 
21827
125
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 A + B = 1679    (1)
 C + D = 118    (2)
- 
21
5000
B + E = 
14741
5000
    (3)
- 
13
125
B + F = 
29173
125
    (4)
 
138
125
A + C = 227    (5)
- 
138
125
A + B -1C = 2030    (6)

Multiply both sides of equation (1) by 138
Divide the two sides of equation (1) by 125, the equation can be obtained:
         
138
125
A + 
138
125
B = 
231702
125
    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 A + B = 1679    (1)
 C + D = 118    (2)
- 
21
5000
B + E = 
14741
5000
    (3)
- 
13
125
B + F = 
29173
125
    (4)
- 
138
125
B + C = - 
203327
125
    (5)
- 
138
125
A + B -1C = 2030    (6)

Multiply both sides of equation (1) by 138
Divide the two sides of equation (1) by 125, the equation can be obtained:
         
138
125
A + 
138
125
B = 
231702
125
    (10)
, then add the two sides of equation (10) to both sides of equation (6), the equations are reduced to:
 A + B = 1679    (1)
 C + D = 118    (2)
- 
21
5000
B + E = 
14741
5000
    (3)
- 
13
125
B + F = 
29173
125
    (4)
- 
138
125
B + C = - 
203327
125
    (5)
 
263
125
B -1C = 
485452
125
    (6)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
- 
13
125
B + F = 
29173
125
    (4)
- 
138
125
B + C = - 
203327
125
    (5)
 
263
125
B -1C = 
485452
125
    (6)

Multiply both sides of equation (2) by 520
Divide the two sides of equation (2) by 21, the equation can be obtained:
        - 
13
125
B + 
520
21
E = 
191633
2625
    (11)
, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
- 
520
21
E + F = 
3368
21
    (4)
- 
138
125
B + C = - 
203327
125
    (5)
 
263
125
B -1C = 
485452
125
    (6)

Multiply both sides of equation (2) by 1840
Divide the two sides of equation (2) by 7, the equation can be obtained:
        - 
138
125
B + 
1840
7
E = 
678086
875
    (12)
, then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
- 
520
21
E + F = 
3368
21
    (4)
 C - 
1840
7
E = - 
16811
7
    (5)
 
263
125
B -1C = 
485452
125
    (6)

Multiply both sides of equation (2) by 10520
Divide the two sides of equation (2) by 21, the equation can be obtained:
        - 
263
125
B + 
10520
21
E = 
3876883
2625
    (13)
, then add the two sides of equation (13) to both sides of equation (6), the equations are reduced to:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
- 
520
21
E + F = 
3368
21
    (4)
 C - 
1840
7
E = - 
16811
7
    (5)
-1C + 
10520
21
E = 
112571
21
    (6)

Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
- 
520
21
E + F = 
3368
21
    (4)
-1D - 
1840
7
E = - 
17637
7
    (5)
-1C + 
10520
21
E = 
112571
21
    (6)

Add both sides of equation (3) to both sides of equation (6) ,the equations are reduced to:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
- 
520
21
E + F = 
3368
21
    (4)
-1D - 
1840
7
E = - 
17637
7
    (5)
 D + 
10520
21
E = 
115049
21
    (6)

交After the exchange of equation (4) and equation (5)， the equation system becomes:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
-1D - 
1840
7
E = - 
17637
7
    (4)
- 
520
21
E + F = 
3368
21
    (5)
 D + 
10520
21
E = 
115049
21
    (6)

Add both sides of equation (4) to both sides of equation (6) ,the equations are reduced to:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
-1D - 
1840
7
E = - 
17637
7
    (4)
- 
520
21
E + F = 
3368
21
    (5)
 
5000
21
E = 
62138
21
    (6)

Multiply both sides of equation (5) by 125
Divide the two sides of equation (5) by 13, the equation can be obtained:
        - 
5000
21
E + 
125
13
F = 
421000
273
    (14)
, then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
-1D - 
1840
7
E = - 
17637
7
    (4)
- 
520
21
E + F = 
3368
21
    (5)
 
125
13
F = 
58514
13
    (6)

Multiply both sides of equation (6) by 13
Divide both sides of equation (6) by 125, get the equation：
         F = 
58514
125
    (15)
, then subtract both sides of equation (15) from both sides of equation (5), get the equation：
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
-1D - 
1840
7
E = - 
17637
7
    (4)
- 
520
21
E = - 
807794
2625
    (5)
 
125
13
F = 
58514
13
    (6)

Multiply both sides of equation (5) by 138
Divide both sides of equation (5) by 13, get the equation：
        - 
1840
7
E = - 
2858348
875
    (16)
, then subtract both sides of equation (16) from both sides of equation (4), get the equation：
 A + B = 1679    (1)
- 
21
5000
B + E = 
14741
5000
    (2)
 C + D = 118    (3)
-1D = 
93389
125
    (4)
- 
520
21
E = - 
807794
2625
    (5)
 F = 
58514
125
    (6)

Multiply both sides of equation (5) by 21
Divide both sides of equation (5) by 520, get the equation：
        -1E = - 
31069
2500
    (17)
, then add the two sides of equation (17) to both sides of equation (2), get the equation：
 A + B = 1679    (1)
- 
21
5000
B = - 
47397
5000
    (2)
 C + D = 118    (3)
-1D = 
93389
125
    (4)
- 
520
21
E = - 
807794
2625
    (5)
 F = 
58514
125
    (6)

Add both sides of equation (4) to both sides of equation (3), get the equation：
 A + B = 1679    (1)
- 
21
5000
B = - 
47397
5000
    (2)
 C = 
108139
125
    (3)
-1D = 
93389
125
    (4)
 E = 
31069
2500
    (5)
 F = 
58514
125
    (6)

Multiply both sides of equation (2) by 5000
Divide both sides of equation (2) by 21, get the equation：
        -1B = -2257    (18)
, then add the two sides of equation (18) to both sides of equation (1), get the equation：
 A = -578    (1)
- 
21
5000
B = - 
47397
5000
    (2)
 C = 
108139
125
    (3)
 D = - 
93389
125
    (4)
 E = 
31069
2500
    (5)
 F = 
58514
125
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = -578    (1)
 B = 2257    (2)
 C = 
108139
125
    (3)
 D = - 
93389
125
    (4)
 E = 
31069
2500
    (5)
 F = 
58514
125
    (6)


Therefore, the solution of the equation set is:
A = -578
B = 2257
C = 
108139
125
D = - 
93389
125
E = 
31069
2500
F = 
58514
125


Convert the solution of the equation set to decimals:
A = -578
B = 2257
C = 865.112000
D = -747.112000
E = 12.427600
F = 468.112000

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。