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 + C + D + E = 
1647
100
    (1)
 D + E = 
9
2
    (2)
 A + B + C = 
1197
100
    (3)
 81600A + 43000B + 31000C + 28000D + 23500E = 467700    (4)
0 = 0    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 A + B + C + D + E = 
1647
100
    (1)
 D + E = 
9
2
    (2)
-1D -1E = - 
9
2
    (3)
 81600A + 43000B + 31000C + 28000D + 23500E = 467700    (4)
0 = 0    (5)

Multiply both sides of equation (1) by 81600, the equation can be obtained:
         81600A + 81600B + 81600C + 81600D + 81600E = 1343952    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 A + B + C + D + E = 
1647
100
    (1)
 D + E = 
9
2
    (2)
-1D -1E = - 
9
2
    (3)
-38600B -50600C -53600D -58100E = -876252    (4)
0 = 0    (5)

交After the exchange of equation (2) and equation (4)， the equation system becomes:
 A + B + C + D + E = 
1647
100
    (1)
-38600B -50600C -53600D -58100E = -876252    (2)
-1D -1E = - 
9
2
    (3)
 D + E = 
9
2
    (4)
0 = 0    (5)

Add both sides of equation (3) to both sides of equation (4) ,the equations are reduced to:
 A + B + C + D + E = 
1647
100
    (1)
-38600B -50600C -53600D -58100E = -876252    (2)
-1D -1E = - 
9
2
    (3)
0 = 0    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 53600, get the equation：
        -53600D -53600E = -241200    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 A + B + C + D + E = 
1647
100
    (1)
-38600B -50600C -4500E = -635052    (2)
-1D -1E = - 
9
2
    (3)
0 = 0    (4)
0 = 0    (5)

Add both sides of equation (3) to both sides of equation (1), get the equation：
 A + B + C = 
1197
100
    (1)
-38600B -50600C -4500E = -635052    (2)
-1D -1E = - 
9
2
    (3)
0 = 0    (4)
0 = 0    (5)

Divide both sides of equation (2) by 38600, get the equation：
        - 
193
193
B - 
253
193
C - 
45
386
E = - 
158763
9650
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 A - 
60
193
C - 
45
386
E = - 
17301
3860
    (1)
-38600B -50600C -4500E = -635052    (2)
 D + E = 
9
2
    (3)
0 = 0    (4)
0 = 0    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A - 
60
193
C - 
45
386
E = - 
17301
3860
    (1)
 B + 
253
193
C + 
45
386
E = 
158763
9650
    (2)
 D + E = 
9
2
    (3)
0 = 0    (4)
0 = 0    (5)


Therefore, the solution of the equation set is:
A = - 
17301
3860
 + 
60
193
C + 
45
386
E
B = 
158763
9650
 - 
253
193
C - 
45
386
E
D = 
9
2
 - 1E


Convert the solution of the equation set to decimals:
A = -4.482124 + 
60
193
C + 
45
386
E
B = 16.452124 - 
253
193
C - 
45
386
E
D = 4.500000 - 1E

Where:  C, E are arbitrary constants.
解方程组的详细方法请参阅：《多元一次方程组的解法》
return