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:
 
33
5
x + 7y + 
73
5
z = 40    (1)
 
33
5
x + 
136
5
y = 40    (2)
 
31
10
x + 
111
10
y = 18    (3)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 
33
5
x + 7y + 
73
5
z = 40    (1)
 
101
5
y - 
73
5
z = 0    (2)
 
31
10
x + 
111
10
y = 18    (3)

Multiply both sides of equation (1) by 31
Divide the two sides of equation (1) by 66, the equation can be obtained:
         
31
10
x + 
217
66
y + 
2263
330
z = 
620
33
    (4)
, then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
 
33
5
x + 7y + 
73
5
z = 40    (1)
 
101
5
y - 
73
5
z = 0    (2)
 
1289
165
y - 
2263
330
z = - 
26
33
    (3)

Multiply both sides of equation (2) by 1289
Divide the two sides of equation (2) by 3333, the equation can be obtained:
         
1289
165
y - 
94097
16665
z = 0    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 
33
5
x + 7y + 
73
5
z = 40    (1)
 
101
5
y - 
73
5
z = 0    (2)
- 
40369
33330
z = - 
2626
3333
    (3)

Multiply both sides of equation (3) by 6666
Divide both sides of equation (3) by 553, get the equation：
        - 
7373
505
z = - 
5252
553
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), get the equation：
 
33
5
x + 7y + 
73
5
z = 40    (1)
 
101
5
y = 
5252
553
    (2)
- 
40369
33330
z = - 
2626
3333
    (3)

Multiply both sides of equation (3) by 6666
Divide both sides of equation (3) by 553, get the equation：
        - 
7373
505
z = - 
5252
553
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
 
33
5
x + 7y = 
16868
553
    (1)
 
101
5
y = 
5252
553
    (2)
- 
40369
33330
z = - 
2626
3333
    (3)

Multiply both sides of equation (2) by 35
Divide both sides of equation (2) by 101, get the equation：
         
707
101
y = 
26260
7979
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 
33
5
x = 
15048
553
    (1)
 
101
5
y = 
5252
553
    (2)
 z = 
26260
40369
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
2280
553
    (1)
 y = 
260
553
    (2)
 z = 
26260
40369
    (3)


Therefore, the solution of the equation set is:
x = 
2280
553
y = 
260
553
z = 
26260
40369


Convert the solution of the equation set to decimals:
x = 4.122966
y = 0.470163
z = 0.650499

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。