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:
 420x + 220y + 200z = 4    (1)
 220x + 520y -200z = 0    (2)
 200x -200y + 500z = 0    (3)
Question solving process:

Multiply both sides of equation (1) by 11
Divide the two sides of equation (1) by 21, the equation can be obtained:
         220x + 
2420
21
y + 
2200
21
z = 
44
21
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 420x + 220y + 200z = 4    (1)
 
8500
21
y - 
6400
21
z = - 
44
21
    (2)
 200x -200y + 500z = 0    (3)

Multiply both sides of equation (1) by 10
Divide the two sides of equation (1) by 21, the equation can be obtained:
         200x + 
2200
21
y + 
2000
21
z = 
40
21
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 420x + 220y + 200z = 4    (1)
 
8500
21
y - 
6400
21
z = - 
44
21
    (2)
- 
6400
21
y + 
8500
21
z = - 
40
21
    (3)

Multiply both sides of equation (2) by 64
Divide the two sides of equation (2) by 85, the equation can be obtained:
         
6400
21
y - 
81920
357
z = - 
2816
1785
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 420x + 220y + 200z = 4    (1)
 
8500
21
y - 
6400
21
z = - 
44
21
    (2)
 
2980
17
z = - 
296
85
    (3)

Multiply both sides of equation (3) by 5440
Divide both sides of equation (3) by 3129, get the equation：
         
953600
3129
z = - 
18944
3129
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 420x + 220y + 200z = 4    (1)
 
8500
21
y = - 
8500
1043
    (2)
 
2980
17
z = - 
296
85
    (3)

Multiply both sides of equation (3) by 170
Divide both sides of equation (3) by 149, get the equation：
         
29800
149
z = - 
592
149
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 420x + 220y = 
1188
149
    (1)
 
8500
21
y = - 
8500
1043
    (2)
 
2980
17
z = - 
296
85
    (3)

Multiply both sides of equation (2) by 231
Divide both sides of equation (2) by 425, get the equation：
         220y = - 
660
149
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 420x = 
1848
149
    (1)
 
8500
21
y = - 
8500
1043
    (2)
 z = - 
74
3725
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
22
745
    (1)
 y = - 
3
149
    (2)
 z = - 
74
3725
    (3)


Therefore, the solution of the equation set is:
x = 
22
745
y = - 
3
149
z = - 
74
3725


Convert the solution of the equation set to decimals:
x = 0.029530
y = -0.020134
z = -0.019866

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。