Mathematics
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Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 A + B = 6    (1)
 C + D = 
37
2
    (2)
 H = 
21
10
    (3)
 E + F + G + H = 
261
10
    (4)
 A + C + E = 
102
25
    (5)
 B + F = 
427
25
    (6)
 D + G = 
652
25
    (7)
 A + B + C + D + E + F + G + H = 
254
5
    (8)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 A + B = 6    (1)
 C + D = 
37
2
    (2)
 H = 
21
10
    (3)
 E + F + G + H = 
261
10
    (4)
-1B + C + E = - 
48
25
    (5)
 B + F = 
427
25
    (6)
 D + G = 
652
25
    (7)
 A + B + C + D + E + F + G + H = 
254
5
    (8)

Subtract both sides of equation (1) from both sides of equation (8) ,the equations are reduced to:
 A + B = 6    (1)
 C + D = 
37
2
    (2)
 H = 
21
10
    (3)
 E + F + G + H = 
261
10
    (4)
-1B + C + E = - 
48
25
    (5)
 B + F = 
427
25
    (6)
 D + G = 
652
25
    (7)
 C + D + E + F + G + H = 
224
5
    (8)

交After the exchange of equation (2) and equation (5)， the equation system becomes:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 H = 
21
10
    (3)
 E + F + G + H = 
261
10
    (4)
 C + D = 
37
2
    (5)
 B + F = 
427
25
    (6)
 D + G = 
652
25
    (7)
 C + D + E + F + G + H = 
224
5
    (8)

Add both sides of equation (2) to both sides of equation (6) ,the equations are reduced to:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 H = 
21
10
    (3)
 E + F + G + H = 
261
10
    (4)
 C + D = 
37
2
    (5)
 C + E + F = 
379
25
    (6)
 D + G = 
652
25
    (7)
 C + D + E + F + G + H = 
224
5
    (8)

交After the exchange of equation (3) and equation (5)， the equation system becomes:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
 E + F + G + H = 
261
10
    (4)
 H = 
21
10
    (5)
 C + E + F = 
379
25
    (6)
 D + G = 
652
25
    (7)
 C + D + E + F + G + H = 
224
5
    (8)

Subtract both sides of equation (3) from both sides of equation (6) ,the equations are reduced to:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
 E + F + G + H = 
261
10
    (4)
 H = 
21
10
    (5)
-1D + E + F = - 
167
50
    (6)
 D + G = 
652
25
    (7)
 C + D + E + F + G + H = 
224
5
    (8)

Subtract both sides of equation (3) from both sides of equation (8) ,the equations are reduced to:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
 E + F + G + H = 
261
10
    (4)
 H = 
21
10
    (5)
-1D + E + F = - 
167
50
    (6)
 D + G = 
652
25
    (7)
 E + F + G + H = 
263
10
    (8)

交After the exchange of equation (4) and equation (6)， the equation system becomes:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
-1D + E + F = - 
167
50
    (4)
 H = 
21
10
    (5)
 E + F + G + H = 
261
10
    (6)
 D + G = 
652
25
    (7)
 E + F + G + H = 
263
10
    (8)

Add both sides of equation (4) to both sides of equation (7) ,the equations are reduced to:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
-1D + E + F = - 
167
50
    (4)
 H = 
21
10
    (5)
 E + F + G + H = 
261
10
    (6)
 E + F + G = 
1137
50
    (7)
 E + F + G + H = 
263
10
    (8)

交After the exchange of equation (5) and equation (6)， the equation system becomes:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
-1D + E + F = - 
167
50
    (4)
 E + F + G + H = 
261
10
    (5)
 H = 
21
10
    (6)
 E + F + G = 
1137
50
    (7)
 E + F + G + H = 
263
10
    (8)

Subtract both sides of equation (5) from both sides of equation (7) ,the equations are reduced to:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
-1D + E + F = - 
167
50
    (4)
 E + F + G + H = 
261
10
    (5)
 H = 
21
10
    (6)
-1H = - 
84
25
    (7)
 E + F + G + H = 
263
10
    (8)

Subtract both sides of equation (5) from both sides of equation (8) ,the equations are reduced to:
 A + B = 6    (1)
-1B + C + E = - 
48
25
    (2)
 C + D = 
37
2
    (3)
-1D + E + F = - 
167
50
    (4)
 E + F + G + H = 
261
10
    (5)
 H = 
21
10
    (6)
-1H = - 
84
25
    (7)
0 = 
1
5
    (8)

由第(8)方程式可以看出，该方程组无解。

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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