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:
 38x -10y -8z = 40    (1)
-10x + 24y = 20    (2)
-8x + 20z = -20    (3)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 19, the equation can be obtained:
         10x - 
50
19
y - 
40
19
z = 
200
19
    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 38x -10y -8z = 40    (1)
 
406
19
y - 
40
19
z = 
580
19
    (2)
-8x + 20z = -20    (3)

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 19, the equation can be obtained:
         8x - 
40
19
y - 
32
19
z = 
160
19
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 38x -10y -8z = 40    (1)
 
406
19
y - 
40
19
z = 
580
19
    (2)
- 
40
19
y + 
348
19
z = - 
220
19
    (3)

Multiply both sides of equation (2) by 20
Divide the two sides of equation (2) by 203, the equation can be obtained:
         
40
19
y - 
800
3857
z = 
400
133
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 38x -10y -8z = 40    (1)
 
406
19
y - 
40
19
z = 
580
19
    (2)
 
3676
203
z = - 
1140
133
    (3)

Multiply both sides of equation (3) by 2030
Divide both sides of equation (3) by 17461, get the equation：
         
36760
17461
z = - 
17400
17461
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 38x -10y -8z = 40    (1)
 
406
19
y = 
515620
17461
    (2)
 
3676
203
z = - 
1140
133
    (3)

Multiply both sides of equation (3) by 406
Divide both sides of equation (3) by 919, get the equation：
         
7352
919
z = - 
3480
919
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 38x -10y = 
33280
919
    (1)
 
406
19
y = 
515620
17461
    (2)
 
3676
203
z = - 
1140
133
    (3)

Multiply both sides of equation (2) by 95
Divide both sides of equation (2) by 203, get the equation：
         10y = 
12700
919
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 38x = 
45980
919
    (1)
 
406
19
y = 
515620
17461
    (2)
 z = - 
435
919
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
1210
919
    (1)
 y = 
1270
919
    (2)
 z = - 
435
919
    (3)


Therefore, the solution of the equation set is:
x = 
1210
919
y = 
1270
919
z = - 
435
919


Convert the solution of the equation set to decimals:
x = 1.316649
y = 1.381937
z = -0.473341

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。