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:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
- 
1
5
A + 
6
5
B - 
1
5
D = 4    (2)
- 
1
5
A + 
1
5
C - 
1
5
D = -2    (3)
- 
1
5
A - 
1
5
B - 
1
5
C + 
6
5
D = 4    (4)
Question solving process:

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 13, the equation can be obtained:
         
1
5
A - 
4
65
B - 
4
65
C - 
4
65
D = - 
8
13
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
- 
1
5
A + 
1
5
C - 
1
5
D = -2    (3)
- 
1
5
A - 
1
5
B - 
1
5
C + 
6
5
D = 4    (4)

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 13, the equation can be obtained:
         
1
5
A - 
4
65
B - 
4
65
C - 
4
65
D = - 
8
13
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
- 
4
65
B + 
9
65
C - 
17
65
D = - 
34
13
    (3)
- 
1
5
A - 
1
5
B - 
1
5
C + 
6
5
D = 4    (4)

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 13, the equation can be obtained:
         
1
5
A - 
4
65
B - 
4
65
C - 
4
65
D = - 
8
13
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
- 
4
65
B + 
9
65
C - 
17
65
D = - 
34
13
    (3)
- 
17
65
B - 
17
65
C + 
74
65
D = 
44
13
    (4)

Multiply both sides of equation (2) by 2
Divide the two sides of equation (2) by 37, the equation can be obtained:
         
4
65
B - 
8
2405
C - 
34
2405
D = 
88
481
    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C - 
51
185
D = - 
90
37
    (3)
- 
17
65
B - 
17
65
C + 
74
65
D = 
44
13
    (4)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 74, the equation can be obtained:
         
17
65
B - 
34
2405
C - 
289
4810
D = 
374
481
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C - 
51
185
D = - 
90
37
    (3)
- 
51
185
C + 
399
370
D = 
154
37
    (4)

Multiply both sides of equation (3) by 51
Divide the two sides of equation (3) by 25, the equation can be obtained:
         
51
185
C - 
2601
4625
D = - 
918
185
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C - 
51
185
D = - 
90
37
    (3)
 
129
250
D = - 
148
185
    (4)

Multiply both sides of equation (4) by 850
Divide both sides of equation (4) by 1591, get the equation：
         
51
185
D = - 
680
1591
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C - 
17
65
D = 
44
13
    (2)
 
5
37
C = - 
4550
1591
    (3)
 
129
250
D = - 
148
185
    (4)

Multiply both sides of equation (4) by 850
Divide both sides of equation (4) by 1677, get the equation：
         
17
65
D = - 
680
1677
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C - 
1
5
D = -2    (1)
 
74
65
B - 
4
65
C = 
4996
1677
    (2)
 
5
37
C = - 
4550
1591
    (3)
 
129
250
D = - 
148
185
    (4)

Multiply both sides of equation (4) by 50
Divide both sides of equation (4) by 129, get the equation：
         
1
5
D = - 
40
129
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C = - 
298
129
    (1)
 
74
65
B - 
4
65
C = 
4996
1677
    (2)
 
5
37
C = - 
4550
1591
    (3)
 
129
250
D = - 
148
185
    (4)

Multiply both sides of equation (3) by 148
Divide both sides of equation (3) by 325, get the equation：
         
4
65
C = - 
56
43
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 
13
20
A - 
1
5
B - 
1
5
C = - 
298
129
    (1)
 
74
65
B = 
2812
1677
    (2)
 
5
37
C = - 
4550
1591
    (3)
 D = - 
200
129
    (4)

Multiply both sides of equation (3) by 37
Divide both sides of equation (3) by 25, get the equation：
         
1
5
C = - 
182
43
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 
13
20
A - 
1
5
B = - 
844
129
    (1)
 
74
65
B = 
2812
1677
    (2)
 
5
37
C = - 
4550
1591
    (3)
 D = - 
200
129
    (4)

Multiply both sides of equation (2) by 13
Divide both sides of equation (2) by 74, get the equation：
         
1
5
B = 
38
129
    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 
13
20
A = - 
806
129
    (1)
 
74
65
B = 
2812
1677
    (2)
 C = - 
910
43
    (3)
 D = - 
200
129
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
1240
129
    (1)
 B = 
190
129
    (2)
 C = - 
910
43
    (3)
 D = - 
200
129
    (4)


Therefore, the solution of the equation set is:
A = - 
1240
129
B = 
190
129
C = - 
910
43
D = - 
200
129


Convert the solution of the equation set to decimals:
A = -9.612403
B = 1.472868
C = -21.162791
D = -1.550388

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。