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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:
 
69
2
A -60B = 0    (1)
 
69
2
A - 
141
10
C = 0    (2)
 
69
2
A -111D = 0    (3)
 
69
2
A -30E = 0    (4)
 69A + 72B + 85C + 170D + 60E = 1000    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
69
2
A -111D = 0    (3)
 
69
2
A -30E = 0    (4)
 69A + 72B + 85C + 170D + 60E = 1000    (5)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 60B -111D = 0    (3)
 
69
2
A -30E = 0    (4)
 69A + 72B + 85C + 170D + 60E = 1000    (5)

Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 60B -111D = 0    (3)
 60B -30E = 0    (4)
 69A + 72B + 85C + 170D + 60E = 1000    (5)

Multiply both sides of equation (1) by 2, the equation can be obtained:
         69A -120B = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (5), the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 60B -111D = 0    (3)
 60B -30E = 0    (4)
 192B + 85C + 170D + 60E = 1000    (5)

Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C -111D = 0    (3)
 60B -30E = 0    (4)
 192B + 85C + 170D + 60E = 1000    (5)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C -111D = 0    (3)
 
141
10
C -30E = 0    (4)
 192B + 85C + 170D + 60E = 1000    (5)

Multiply both sides of equation (2) by 16
Divide the two sides of equation (2) by 5, the equation can be obtained:
         192B - 
1128
25
C = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (5), the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C -111D = 0    (3)
 
141
10
C -30E = 0    (4)
 
3253
25
C + 170D + 60E = 1000    (5)

Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C -111D = 0    (3)
 111D -30E = 0    (4)
 
3253
25
C + 170D + 60E = 1000    (5)

Multiply both sides of equation (3) by 6506
Divide the two sides of equation (3) by 705, the equation can be obtained:
         
3253
25
C - 
240722
235
D = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C -111D = 0    (3)
 111D -30E = 0    (4)
 
280672
235
D + 60E = 1000    (5)

Multiply both sides of equation (4) by 280672
Divide the two sides of equation (4) by 26085, the equation can be obtained:
         
280672
235
D - 
561344
1739
E = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C -111D = 0    (3)
 111D -30E = 0    (4)
 
665684
1739
E = 1000    (5)

Multiply both sides of equation (5) by 26085
Divide both sides of equation (5) by 332842, get the equation：
         
13830
461
E = 
13042500
166421
    (10)
, then add the two sides of equation (10) to both sides of equation (4), get the equation：
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C -111D = 0    (3)
 111D = 
13042500
166421
    (4)
 
665684
1739
E = 1000    (5)

Add both sides of equation (4) to both sides of equation (3), get the equation：
 
69
2
A -60B = 0    (1)
 60B - 
141
10
C = 0    (2)
 
141
10
C = 
13042500
166421
    (3)
 111D = 
13042500
166421
    (4)
 E = 
434750
166421
    (5)

Add both sides of equation (3) to both sides of equation (2), get the equation：
 
69
2
A -60B = 0    (1)
 60B = 
13042500
166421
    (2)
 
141
10
C = 
13042500
166421
    (3)
 D = 
117500
166421
    (4)
 E = 
434750
166421
    (5)

Add both sides of equation (2) to both sides of equation (1), get the equation：
 
69
2
A = 
13042500
166421
    (1)
 60B = 
13042500
166421
    (2)
 C = 
925000
166421
    (3)
 D = 
117500
166421
    (4)
 E = 
434750
166421
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
8695000
3827683
    (1)
 B = 
217375
166421
    (2)
 C = 
925000
166421
    (3)
 D = 
117500
166421
    (4)
 E = 
434750
166421
    (5)


Therefore, the solution of the equation set is:
A = 
8695000
3827683
B = 
217375
166421
C = 
925000
166421
D = 
117500
166421
E = 
434750
166421


Convert the solution of the equation set to decimals:
A = 2.271609
B = 1.306175
C = 5.558193
D = 0.706041
E = 2.612351

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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