Mathematics
         
语言:中文    Language:English
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:
 6x -2y = 345    (1)
-2x + 4y -2z = 25    (2)
-2y + 
6111
2500
z = 
4518
125
    (3)
Question solving process:

Divide the two sides of equation (1) by 3, the equation can be obtained:
         2x 
2
3
y = 115    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 6x -2y = 345    (1)
 
10
3
y -2z = 140    (2)
-2y + 
6111
2500
z = 
4518
125
    (3)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 5, the equation can be obtained:
         2y 
6
5
z = 84    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 6x -2y = 345    (1)
 
10
3
y -2z = 140    (2)
 
3111
2500
z = 
15018
125
    (3)

Multiply both sides of equation (3) by 5000
Divide both sides of equation (3) by 3111, get the equation:
         2z = 
200240
1037
    (6)
, then add the two sides of equation (6) to both sides of equation (2), get the equation:
 6x -2y = 345    (1)
 
10
3
y = 
345420
1037
    (2)
 
3111
2500
z = 
15018
125
    (3)

Multiply both sides of equation (2) by 3
Divide both sides of equation (2) by 5, get the equation:
         2y = 
207252
1037
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation:
 6x = 
565017
1037
    (1)
 
10
3
y = 
345420
1037
    (2)
 z = 
100120
1037
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
188339
2074
    (1)
 y = 
103626
1037
    (2)
 z = 
100120
1037
    (3)


Therefore, the solution of the equation set is:
x = 
188339
2074
y = 
103626
1037
z = 
100120
1037


Convert the solution of the equation set to decimals:
x = 90.809547
y = 99.928640
z = 96.547734

解方程组的详细方法请参阅:《多元一次方程组的解法》







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