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:
 40x -20y 
1
2
z = -7    (1)
 61y + 
1
2
z = 91    (2)
 20x + z = 0    (3)
Question solving process:

Divide the two sides of equation (1) by 2, the equation can be obtained:
         20x -10y 
1
4
z = 
7
2
    (4)
, then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
 40x -20y 
1
2
z = -7    (1)
 61y + 
1
2
z = 91    (2)
 10y + 
5
4
z = 
7
2
    (3)

Multiply both sides of equation (2) by 10
Divide the two sides of equation (2) by 61, the equation can be obtained:
         10y + 
5
61
z = 
910
61
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 40x -20y 
1
2
z = -7    (1)
 61y + 
1
2
z = 91    (2)
 
285
244
z = 
1393
122
    (3)

Multiply both sides of equation (3) by 122
Divide both sides of equation (3) by 285, get the equation:
         
1
2
z = 
1393
285
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), get the equation:
 40x -20y 
1
2
z = -7    (1)
 61y = 
27328
285
    (2)
 
285
244
z = 
1393
122
    (3)

Multiply both sides of equation (3) by 122
Divide both sides of equation (3) by 285, get the equation:
         
1
2
z = 
1393
285
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation:
 40x -20y = 
3388
285
    (1)
 61y = 
27328
285
    (2)
 
285
244
z = 
1393
122
    (3)

Multiply both sides of equation (2) by 20
Divide both sides of equation (2) by 61, get the equation:
         20y = 
1792
57
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 40x = 
5572
285
    (1)
 61y = 
27328
285
    (2)
 z = 
2786
285
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
1393
2850
    (1)
 y = 
448
285
    (2)
 z = 
2786
285
    (3)


Therefore, the solution of the equation set is:
x = 
1393
2850
y = 
448
285
z = 
2786
285


Convert the solution of the equation set to decimals:
x = 0.488772
y = 1.571930
z = -9.775439

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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