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:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
 A + 
7
100
B + 
7
100
C + E = 0    (2)
 A = 0    (3)
 A = 0    (4)
 A = 0    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
 A = 0    (3)
 A = 0    (4)
 A = 0    (5)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (3)
 A = 0    (4)
 A = 0    (5)

Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (3)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (4)
 A = 0    (5)

Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (3)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (4)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (5)

Multiply both sides of equation (2) by 79
Divide the two sides of equation (2) by 72, the equation can be obtained:
        
79
100
B 
79
144
C 
8453
7200
D 
553
7200
E = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (3)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (4)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (5)

Multiply both sides of equation (2) by 79
Divide the two sides of equation (2) by 72, the equation can be obtained:
        
79
100
B 
79
144
C 
8453
7200
D 
553
7200
E = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (3)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (4)
79
100
B 
57
100
C 
107
100
D 
107
100
E = 0    (5)

Multiply both sides of equation (2) by 79
Divide the two sides of equation (2) by 72, the equation can be obtained:
        
79
100
B 
79
144
C 
8453
7200
D 
553
7200
E = 0    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (3)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (4)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (5)

Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (3)
0 = 0    (4)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (5)

Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
1
2
C 
107
100
D 
7
100
E = 0    (2)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (3)
0 = 0    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 1800
Divide both sides of equation (3) by 77, get the equation:
        
1
2
C + 
107
44
D 
7151
308
E = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 A + 
79
100
B + 
57
100
C + 
107
100
D + 
107
100
E = 0    (1)
18
25
B 
963
275
D + 
44559
1925
E = 0    (2)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (3)
0 = 0    (4)
0 = 0    (5)

Multiply both sides of equation (3) by 2052
Divide both sides of equation (3) by 77, get the equation:
        
57
100
C + 
6099
2200
D 
407607
15400
E = 0    (10)
, then add the two sides of equation (10) to both sides of equation (1), get the equation:
 A + 
79
100
B + 
8453
2200
D 
391129
15400
E = 0    (1)
18
25
B 
963
275
D + 
44559
1925
E = 0    (2)
77
3600
C + 
749
7200
D 
7151
7200
E = 0    (3)
0 = 0    (4)
0 = 0    (5)

Multiply both sides of equation (2) by 79
Divide both sides of equation (2) by 72, get the equation:
        
79
100
B 
8453
2200
D + 
391129
15400
E = 0    (11)
, then add the two sides of equation (11) to both sides of equation (1), get the equation:
 A = 0    (1)
18
25
B 
963
275
D + 
44559
1925
E = 0    (2)
 C 
107
22
D + 
7151
154
E = 0    (3)
0 = 0    (4)
0 = 0    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 0    (1)
 B + 
107
22
D 
4951
154
E = 0    (2)
 C 
107
22
D + 
7151
154
E = 0    (3)
0 = 0    (4)
0 = 0    (5)


Therefore, the solution of the equation set is:
A = 0
B = -
107
22
D + 
4951
154
E
C = 
107
22
D - 
7151
154
E

Where:  D, E 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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