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:
- 
162
125
x + 
7
25
y + 
7
25
z = 0    (1)
 
7
25
x - 
7
25
y + 
7
25
z = 0    (2)
 x + y + z = 1    (3)
Question solving process:

Multiply both sides of equation (1) by 35
Divide the two sides of equation (1) by 162, the equation can be obtained:
        - 
7
25
x + 
49
810
y + 
49
810
z = 0    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
- 
162
125
x + 
7
25
y + 
7
25
z = 0    (1)
- 
889
4050
y + 
1379
4050
z = 0    (2)
 x + y + z = 1    (3)

Multiply both sides of equation (1) by 125
Divide the two sides of equation (1) by 162, the equation can be obtained:
        -1x + 
35
162
y + 
35
162
z = 0    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
- 
162
125
x + 
7
25
y + 
7
25
z = 0    (1)
- 
889
4050
y + 
1379
4050
z = 0    (2)
 
197
162
y + 
197
162
z = 1    (3)

Multiply both sides of equation (2) by 4925
Divide the two sides of equation (2) by 889, the equation can be obtained:
        - 
197
162
y + 
38809
20574
z = 0    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
- 
162
125
x + 
7
25
y + 
7
25
z = 0    (1)
- 
889
4050
y + 
1379
4050
z = 0    (2)
 
394
127
z = 
127
127
    (3)

Multiply both sides of equation (3) by 175133
Divide both sides of equation (3) by 1595700, get the equation：
         
1379
4050
z = 
889
8100
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
- 
162
125
x + 
7
25
y + 
7
25
z = 0    (1)
- 
889
4050
y = - 
889
8100
    (2)
 
394
127
z = 
127
127
    (3)

Multiply both sides of equation (3) by 889
Divide both sides of equation (3) by 9850, get the equation：
         
1379
4925
z = 
889
9850
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
- 
162
125
x + 
7
25
y = - 
889
9850
    (1)
- 
889
4050
y = - 
889
8100
    (2)
 
394
127
z = 
127
127
    (3)

Multiply both sides of equation (2) by 162
Divide both sides of equation (2) by 127, get the equation：
        - 
889
3175
y = - 
889
6350
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
- 
162
125
x = - 
1134
4925
    (1)
- 
889
4050
y = - 
889
8100
    (2)
 z = 
127
394
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
35
197
    (1)
 y = 
127
254
    (2)
 z = 
127
394
    (3)


Therefore, the solution of the equation set is:
x = 
35
197
y = 
127
254
z = 
127
394


Convert the solution of the equation set to decimals:
x = 0.177665
y = 0.500000
z = 0.322335

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。