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:
 
47
5
x + 
221
5
y + 
23
2
z = 
7543
500
    (1)
 
43
50
x + 
143
50
y + 
43
50
z = 
93
50
    (2)
0 = 0    (3)
Question solving process:

Multiply both sides of equation (1) by 43
Divide the two sides of equation (1) by 470, the equation can be obtained:
         
43
50
x + 
9503
2350
y + 
989
940
z = 
324349
235000
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 
47
5
x + 
221
5
y + 
23
2
z = 
7543
500
    (1)
1391
1175
y 
903
4700
z = 
112751
235000
    (2)
0 = 0    (3)

Multiply both sides of equation (2) by 3995
Divide both sides of equation (2) by 107, get the equation:
        
23647
535
y 
15351
2140
z = 
1916767
107000
    (5)
, then add the two sides of equation (5) to both sides of equation (1), get the equation:
 
47
5
x + 
9259
2140
z = 
3530969
107000
    (1)
1391
1175
y 
903
4700
z = 
112751
235000
    (2)
0 = 0    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x + 
197
428
z = 
75127
21400
    (1)
 y + 
903
5564
z = 
112751
278200
    (2)
0 = 0    (3)


Therefore, the solution of the equation set is:
x = 
75127
21400
 - 
197
428
z
y = 
112751
278200
 - 
903
5564
z


Convert the solution of the equation set to decimals:
x = 3.510607 - 
197
428
z
y = -0.405288 - 
903
5564
z

Where:  z are arbitrary constants.
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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