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 -1D = 0    (1)
 A -1C = 10    (2)
-330A + 510B = 12    (3)
 330A + 510C + 10D = 12    (4)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 A + B -1D = 0    (1)
-1B -1C + D = 10    (2)
-330A + 510B = 12    (3)
 330A + 510C + 10D = 12    (4)

Multiply both sides of equation (1) by 330, the equation can be obtained:
         330A + 330B -330D = 0    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 A + B -1D = 0    (1)
-1B -1C + D = 10    (2)
 840B -330D = 12    (3)
 330A + 510C + 10D = 12    (4)

Multiply both sides of equation (1) by 330, the equation can be obtained:
         330A + 330B -330D = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 A + B -1D = 0    (1)
-1B -1C + D = 10    (2)
 840B -330D = 12    (3)
-330B + 510C + 340D = 12    (4)

Multiply both sides of equation (2) by 840, the equation can be obtained:
        -840B -840C + 840D = 8400    (7)
, then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 A + B -1D = 0    (1)
-1B -1C + D = 10    (2)
-840C + 510D = 8412    (3)
-330B + 510C + 340D = 12    (4)

Multiply both sides of equation (2) by 330, the equation can be obtained:
        -330B -330C + 330D = 3300    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 A + B -1D = 0    (1)
-1B -1C + D = 10    (2)
-840C + 510D = 8412    (3)
 840C + 10D = -3288    (4)

Add both sides of equation (3) to both sides of equation (4) ,the equations are reduced to:
 A + B -1D = 0    (1)
-1B -1C + D = 10    (2)
-840C + 510D = 8412    (3)
 520D = 5124    (4)

Multiply both sides of equation (4) by 51
Divide both sides of equation (4) by 52, get the equation：
         510D = 
65331
13
    (9)
, then subtract both sides of equation (9) from both sides of equation (3), get the equation：
 A + B -1D = 0    (1)
-1B -1C + D = 10    (2)
-840C = 
44025
13
    (3)
 520D = 5124    (4)

Divide both sides of equation (4) by 520, get the equation：
         D = 
1281
130
    (10)
, then subtract both sides of equation (10) from both sides of equation (2), get the equation：
 A + B -1D = 0    (1)
-1B -1C = 
19
130
    (2)
-840C = 
44025
13
    (3)
 520D = 5124    (4)

Divide both sides of equation (4) by 520, get the equation：
         D = 
1281
130
    (11)
, then add the two sides of equation (11) to both sides of equation (1), get the equation：
 A + B = 
1281
130
    (1)
-1B -1C = 
19
130
    (2)
-840C = 
44025
13
    (3)
 520D = 5124    (4)

Divide both sides of equation (3) by 840, get the equation：
        -1C = 
2935
728
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 A + B = 
1281
130
    (1)
-1B = - 
14143
3640
    (2)
-840C = 
44025
13
    (3)
 D = 
1281
130
    (4)

Add both sides of equation (2) to both sides of equation (1), get the equation：
 A = 
4345
728
    (1)
-1B = - 
14143
3640
    (2)
 C = - 
2935
728
    (3)
 D = 
1281
130
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
4345
728
    (1)
 B = 
14143
3640
    (2)
 C = - 
2935
728
    (3)
 D = 
1281
130
    (4)


Therefore, the solution of the equation set is:
A = 
4345
728
B = 
14143
3640
C = - 
2935
728
D = 
1281
130


Convert the solution of the equation set to decimals:
A = 5.968407
B = 3.885440
C = -4.031593
D = 9.853846

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。