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:
 
3111
10000
x - 
1
10
y = - 
1
10
    (1)
- 
1
10
y + 
1
10
z = - 
1
10
    (2)
- 
1
10
x + 
11
10
y - 
1
10
z = - 
1
10
    (3)
Question solving process:

Multiply both sides of equation (1) by 1000
Divide the two sides of equation (1) by 3111, the equation can be obtained:
         
1
10
x - 
100
3111
y = - 
100
3111
    (4)
, then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
 
3111
10000
x - 
1
10
y = - 
1
10
    (1)
- 
1
10
y + 
1
10
z = - 
1
10
    (2)
 
33221
31110
y - 
1
10
z = - 
4111
31110
    (3)

Multiply both sides of equation (2) by 33221
Divide the two sides of equation (2) by 3111, the equation can be obtained:
        - 
33221
31110
y + 
33221
31110
z = - 
33221
31110
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 
3111
10000
x - 
1
10
y = - 
1
10
    (1)
- 
1
10
y + 
1
10
z = - 
1
10
    (2)
 
3011
3111
z = - 
366
305
    (3)

Multiply both sides of equation (3) by 3111
Divide both sides of equation (3) by 30110, get the equation：
         
3011
30110
z = - 
9333
75275
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), get the equation：
 
3111
10000
x - 
1
10
y = - 
1
10
    (1)
- 
1
10
y = 
3611
150550
    (2)
 
3011
3111
z = - 
366
305
    (3)

Subtract both sides of equation (2) from both sides of equation (1), get the equation：
 
3111
10000
x = - 
9333
75275
    (1)
- 
1
10
y = 
3611
150550
    (2)
 z = - 
18666
15055
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
1200
3011
    (1)
 y = - 
3611
15055
    (2)
 z = - 
18666
15055
    (3)


Therefore, the solution of the equation set is:
x = - 
1200
3011
y = - 
3611
15055
z = - 
18666
15055


Convert the solution of the equation set to decimals:
x = -0.398539
y = -0.239854
z = -1.239854

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。