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:
 10x + 5y = 
1146789
50
    (1)
 17x + 5y + 6z = 
557103
20
    (2)
 13x + 5y + 8z = 
506329
20
    (3)
Question solving process:

Multiply both sides of equation (1) by 17
Divide the two sides of equation (1) by 10, the equation can be obtained:
         17x + 
17
2
y = 
19495413
500
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 10x + 5y = 
1146789
50
    (1)
- 
7
2
y + 6z = - 
2783919
250
    (2)
 13x + 5y + 8z = 
506329
20
    (3)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 10, the equation can be obtained:
         13x + 
13
2
y = 
14908257
500
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 10x + 5y = 
1146789
50
    (1)
- 
7
2
y + 6z = - 
2783919
250
    (2)
- 
3
2
y + 8z = - 
562508
125
    (3)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 7, the equation can be obtained:
        - 
3
2
y + 
18
7
z = - 
8351757
1750
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 10x + 5y = 
1146789
50
    (1)
- 
7
2
y + 6z = - 
2783919
250
    (2)
 
38
7
z = 
95329
350
    (3)

Multiply both sides of equation (3) by 21
Divide both sides of equation (3) by 19, get the equation：
         6z = 
285987
950
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 10x + 5y = 
1146789
50
    (1)
- 
7
2
y = - 
27162198
2375
    (2)
 
38
7
z = 
95329
350
    (3)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 7, get the equation：
        -5y = - 
7760628
475
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 10x = 
1253547
190
    (1)
- 
7
2
y = - 
27162198
2375
    (2)
 z = 
95329
1900
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
1253547
1900
    (1)
 y = 
7760628
2375
    (2)
 z = 
95329
1900
    (3)


Therefore, the solution of the equation set is:
x = 
1253547
1900
y = 
7760628
2375
z = 
95329
1900


Convert the solution of the equation set to decimals:
x = 659.761579
y = 3267.632842
z = 50.173158

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。