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:
 2A + 3B + 4C + 5D = 27    (1)
 5A + 4B + C = 12    (2)
 4A + 3C + 6D = 18    (3)
 3A + 7B + 4C = 17    (4)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 2, the equation can be obtained:
         5A + 
15
2
B + 10C + 
25
2
D = 
135
2
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C - 
25
2
D = - 
111
2
    (2)
 4A + 3C + 6D = 18    (3)
 3A + 7B + 4C = 17    (4)

Multiply both sides of equation (1) by 2, the equation can be obtained:
         4A + 6B + 8C + 10D = 54    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C - 
25
2
D = - 
111
2
    (2)
-6B -5C -4D = -36    (3)
 3A + 7B + 4C = 17    (4)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         3A + 
9
2
B + 6C + 
15
2
D = 
81
2
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C - 
25
2
D = - 
111
2
    (2)
-6B -5C -4D = -36    (3)
 
5
2
B -2C - 
15
2
D = - 
47
2
    (4)

Multiply both sides of equation (2) by 12
Divide the two sides of equation (2) by 7, the equation can be obtained:
        -6B - 
108
7
C - 
150
7
D = - 
666
7
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C - 
25
2
D = - 
111
2
    (2)
 
73
7
C + 
122
7
D = 
414
7
    (3)
 
5
2
B -2C - 
15
2
D = - 
47
2
    (4)

Multiply both sides of equation (2) by 5
Divide the two sides of equation (2) by 7, the equation can be obtained:
        - 
5
2
B - 
45
7
C - 
125
14
D = - 
555
14
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C - 
25
2
D = - 
111
2
    (2)
 
73
7
C + 
122
7
D = 
414
7
    (3)
- 
59
7
C - 
115
7
D = - 
442
7
    (4)

Multiply both sides of equation (3) by 59
Divide the two sides of equation (3) by 73, the equation can be obtained:
         
59
7
C + 
7198
511
D = 
24426
511
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C - 
25
2
D = - 
111
2
    (2)
 
73
7
C + 
122
7
D = 
414
7
    (3)
- 
171
73
D = - 
1120
73
    (4)

Multiply both sides of equation (4) by 8906
Divide both sides of equation (4) by 1197, get the equation：
        - 
122
7
D = - 
19520
171
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C - 
25
2
D = - 
111
2
    (2)
 
73
7
C = - 
65846
1197
    (3)
- 
171
73
D = - 
1120
73
    (4)

Multiply both sides of equation (4) by 1825
Divide both sides of equation (4) by 342, get the equation：
        - 
25
2
D = - 
14000
171
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 2A + 3B + 4C + 5D = 27    (1)
- 
7
2
B -9C = 
9019
342
    (2)
 
73
7
C = - 
65846
1197
    (3)
- 
171
73
D = - 
1120
73
    (4)

Multiply both sides of equation (4) by 365
Divide both sides of equation (4) by 171, get the equation：
        -5D = - 
5600
171
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 2A + 3B + 4C = - 
983
171
    (1)
- 
7
2
B -9C = 
9019
342
    (2)
 
73
7
C = - 
65846
1197
    (3)
- 
171
73
D = - 
1120
73
    (4)

Multiply both sides of equation (3) by 63
Divide both sides of equation (3) by 73, get the equation：
         9C = - 
902
19
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 2A + 3B + 4C = - 
983
171
    (1)
- 
7
2
B = - 
7217
342
    (2)
 
73
7
C = - 
65846
1197
    (3)
 D = 
1120
171
    (4)

Multiply both sides of equation (3) by 28
Divide both sides of equation (3) by 73, get the equation：
         4C = - 
3608
171
    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation：
 2A + 3B = 
875
57
    (1)
- 
7
2
B = - 
7217
342
    (2)
 
73
7
C = - 
65846
1197
    (3)
 D = 
1120
171
    (4)

Multiply both sides of equation (2) by 6
Divide both sides of equation (2) by 7, get the equation：
        -3B = - 
1031
57
    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 2A = - 
52
19
    (1)
- 
7
2
B = - 
7217
342
    (2)
 C = - 
902
171
    (3)
 D = 
1120
171
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
26
19
    (1)
 B = 
1031
171
    (2)
 C = - 
902
171
    (3)
 D = 
1120
171
    (4)


Therefore, the solution of the equation set is:
A = - 
26
19
B = 
1031
171
C = - 
902
171
D = 
1120
171


Convert the solution of the equation set to decimals:
A = -1.368421
B = 6.029240
C = -5.274854
D = 6.549708

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。