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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:
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
 
2
5
A + 
1
2
D + 
1
2
E = 99    (2)
 
1
2
C + 
1
2
D + 
1
2
E = 120    (3)
 
1
2
B + 
1
2
C + 
1
2
E = 123    (4)
 
1
2
C + 
1
2
E = 41    (5)
Question solving process:

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 7, the equation can be obtained:
         
2
5
A + 
6
35
B + 
6
35
E = 
464
7
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D + 
23
70
E = 
229
7
    (2)
 
1
2
C + 
1
2
D + 
1
2
E = 120    (3)
 
1
2
B + 
1
2
C + 
1
2
E = 123    (4)
 
1
2
C + 
1
2
E = 41    (5)

Multiply both sides of equation (2) by 35
Divide the two sides of equation (2) by 12, the equation can be obtained:
        - 
1
2
B + 
35
24
D + 
23
24
E = 
1145
12
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D + 
23
70
E = 
229
7
    (2)
 
1
2
C + 
1
2
D + 
1
2
E = 120    (3)
 
1
2
C + 
35
24
D + 
35
24
E = 
2621
12
    (4)
 
1
2
C + 
1
2
E = 41    (5)

Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D + 
23
70
E = 
229
7
    (2)
 
1
2
C + 
1
2
D + 
1
2
E = 120    (3)
 
23
24
D + 
23
24
E = 
1181
12
    (4)
 
1
2
C + 
1
2
E = 41    (5)

Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D + 
23
70
E = 
229
7
    (2)
 
1
2
C + 
1
2
D + 
1
2
E = 120    (3)
 
23
24
D + 
23
24
E = 
1181
12
    (4)
- 
1
2
D = -79    (5)

Multiply both sides of equation (4) by 12
Divide the two sides of equation (4) by 23, the equation can be obtained:
         
1
2
D + 
1
2
E = 
1181
23
    (8)
, then add the two sides of equation (8) to both sides of equation (5), the equations are reduced to:
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D + 
23
70
E = 
229
7
    (2)
 
1
2
C + 
1
2
D + 
1
2
E = 120    (3)
 
23
24
D + 
23
24
E = 
1181
12
    (4)
 
1
2
E = - 
636
23
    (5)

Multiply both sides of equation (5) by 23
Divide both sides of equation (5) by 12, get the equation：
         
23
24
E = -53    (9)
, then subtract both sides of equation (9) from both sides of equation (4), get the equation：
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D + 
23
70
E = 
229
7
    (2)
 
1
2
C + 
1
2
D + 
1
2
E = 120    (3)
 
23
24
D = 
1817
12
    (4)
 
1
2
E = - 
636
23
    (5)

Subtract both sides of equation (5) from both sides of equation (3), get the equation：
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D + 
23
70
E = 
229
7
    (2)
 
1
2
C + 
1
2
D = 
3396
23
    (3)
 
23
24
D = 
1817
12
    (4)
 
1
2
E = - 
636
23
    (5)

Multiply both sides of equation (5) by 23
Divide both sides of equation (5) by 35, get the equation：
         
23
70
E = - 
636
35
    (10)
, then subtract both sides of equation (10) from both sides of equation (2), get the equation：
 
7
10
A + 
3
10
B + 
3
10
E = 116    (1)
- 
6
35
B + 
1
2
D = 
1781
35
    (2)
 
1
2
C + 
1
2
D = 
3396
23
    (3)
 
23
24
D = 
1817
12
    (4)
 
1
2
E = - 
636
23
    (5)

Multiply both sides of equation (5) by 3
Divide both sides of equation (5) by 5, get the equation：
         
3
10
E = - 
1908
115
    (11)
, then subtract both sides of equation (11) from both sides of equation (1), get the equation：
 
7
10
A + 
3
10
B = 
15248
115
    (1)
- 
6
35
B + 
1
2
D = 
1781
35
    (2)
 
1
2
C + 
1
2
D = 
3396
23
    (3)
 
23
24
D = 
1817
12
    (4)
 
1
2
E = - 
636
23
    (5)

Multiply both sides of equation (4) by 12
Divide both sides of equation (4) by 23, get the equation：
         
1
2
D = 79    (12)
, then subtract both sides of equation (12) from both sides of equation (3), get the equation：
 
7
10
A + 
3
10
B = 
15248
115
    (1)
- 
6
35
B + 
1
2
D = 
1781
35
    (2)
 
1
2
C = 
1579
23
    (3)
 
23
24
D = 
1817
12
    (4)
 E = - 
1272
23
    (5)

Multiply both sides of equation (4) by 12
Divide both sides of equation (4) by 23, get the equation：
         
1
2
D = 79    (13)
, then subtract both sides of equation (13) from both sides of equation (2), get the equation：
 
7
10
A + 
3
10
B = 
15248
115
    (1)
- 
6
35
B = - 
984
35
    (2)
 
1
2
C = 
1579
23
    (3)
 
23
24
D = 
1817
12
    (4)
 E = - 
1272
23
    (5)

Multiply both sides of equation (2) by 7
Divide both sides of equation (2) by 4, get the equation：
        - 
3
10
B = - 
246
5
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 
7
10
A = 
1918
23
    (1)
- 
6
35
B = - 
984
35
    (2)
 C = 
3158
23
    (3)
 D = 158    (4)
 E = - 
1272
23
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
2740
23
    (1)
 B = 164    (2)
 C = 
3158
23
    (3)
 D = 158    (4)
 E = - 
1272
23
    (5)


Therefore, the solution of the equation set is:
A = 
2740
23
B = 164
C = 
3158
23
D = 158
E = - 
1272
23


Convert the solution of the equation set to decimals:
A = 119.130435
B = 164
C = 137.304348
D = 158
E = -55.304348

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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