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:
 
403
5
x + 
155
2
y + 
149
2
z = 
783
10
    (1)
 
427
5
x + 
407
5
y + 
382
5
z = 
412
5
    (2)
 
427
5
x + 
397
5
y + 
347
5
z = 
402
5
    (3)
Question solving process:

Multiply both sides of equation (1) by 427
Divide the two sides of equation (1) by 403, the equation can be obtained:
         
427
5
x + 
66185
806
y + 
63623
806
z = 
334341
4030
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 
403
5
x + 
155
2
y + 
149
2
z = 
783
10
    (1)
- 
93
130
y - 
10223
4030
z = - 
2269
4030
    (2)
 
427
5
x + 
397
5
y + 
347
5
z = 
402
5
    (3)

Multiply both sides of equation (1) by 427
Divide the two sides of equation (1) by 403, the equation can be obtained:
         
427
5
x + 
66185
806
y + 
63623
806
z = 
334341
4030
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 
403
5
x + 
155
2
y + 
149
2
z = 
783
10
    (1)
- 
93
130
y - 
10223
4030
z = - 
2269
4030
    (2)
- 
353
130
y - 
38433
4030
z = - 
10329
4030
    (3)

Multiply both sides of equation (2) by 353
Divide the two sides of equation (2) by 93, the equation can be obtained:
        - 
353
130
y - 
3608719
374790
z = - 
800957
374790
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 
403
5
x + 
155
2
y + 
149
2
z = 
783
10
    (1)
- 
93
130
y - 
10223
4030
z = - 
2269
4030
    (2)
 
265
2883
z = - 
1228
2883
    (3)

Multiply both sides of equation (3) by 950739
Divide both sides of equation (3) by 34450, get the equation：
         
10223
4030
z = - 
6276922
533975
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 
403
5
x + 
155
2
y + 
149
2
z = 
783
10
    (1)
- 
93
130
y = - 
32643
2650
    (2)
 
265
2883
z = - 
1228
2883
    (3)

Multiply both sides of equation (3) by 429567
Divide both sides of equation (3) by 530, get the equation：
         
149
2
z = - 
91486
265
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 
403
5
x + 
155
2
y = 
224471
530
    (1)
- 
93
130
y = - 
32643
2650
    (2)
 
265
2883
z = - 
1228
2883
    (3)

Multiply both sides of equation (2) by 325
Divide both sides of equation (2) by 3, get the equation：
        - 
155
2
y = - 
141453
106
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 
403
5
x = - 
241397
265
    (1)
- 
93
130
y = - 
32643
2650
    (2)
 z = - 
1228
265
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
599
53
    (1)
 y = 
4563
265
    (2)
 z = - 
1228
265
    (3)


Therefore, the solution of the equation set is:
x = - 
599
53
y = 
4563
265
z = - 
1228
265


Convert the solution of the equation set to decimals:
x = -11.301887
y = 17.218868
z = -4.633962

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。