Mathematics
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Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 A + 3B + 4C + 4D = 
377
250
    (1)
 A + 5B + 6C + 6D = 
567
250
    (2)
 A + 4B + 5C + 7D = 
567
250
    (3)
 A + 7B + 6C + 8D = 
567
250
    (4)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 A + 3B + 4C + 4D = 
377
250
    (1)
 2B + 2C + 2D = 
19
25
    (2)
 A + 4B + 5C + 7D = 
567
250
    (3)
 A + 7B + 6C + 8D = 
567
250
    (4)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 A + 3B + 4C + 4D = 
377
250
    (1)
 2B + 2C + 2D = 
19
25
    (2)
 B + C + 3D = 
19
25
    (3)
 A + 7B + 6C + 8D = 
567
250
    (4)

Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 A + 3B + 4C + 4D = 
377
250
    (1)
 2B + 2C + 2D = 
19
25
    (2)
 B + C + 3D = 
19
25
    (3)
 4B + 2C + 4D = 
19
25
    (4)

Divide the two sides of equation (2) by 2, the equation can be obtained:
         B + C + D = 
19
50
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 A + 3B + 4C + 4D = 
377
250
    (1)
 2B + 2C + 2D = 
19
25
    (2)
 2D = 
19
50
    (3)
 4B + 2C + 4D = 
19
25
    (4)

Multiply both sides of equation (2) by 2, the equation can be obtained:
         4B + 4C + 4D = 
38
25
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 A + 3B + 4C + 4D = 
377
250
    (1)
 2B + 2C + 2D = 
19
25
    (2)
 2D = 
19
50
    (3)
-2C = - 
19
25
    (4)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 A + 3B + 4C + 4D = 
377
250
    (1)
 2B + 2C + 2D = 
19
25
    (2)
-2C = - 
19
25
    (3)
 2D = 
19
50
    (4)

Subtract both sides of equation (4) from both sides of equation (2), get the equation：
 A + 3B + 4C + 4D = 
377
250
    (1)
 2B + 2C = 
19
50
    (2)
-2C = - 
19
25
    (3)
 2D = 
19
50
    (4)

Multiply both sides of equation (4) by 2, get the equation：
         4D = 
19
25
    (7)
, then subtract both sides of equation (7) from both sides of equation (1), get the equation：
 A + 3B + 4C = 
187
250
    (1)
 2B + 2C = 
19
50
    (2)
-2C = - 
19
25
    (3)
 2D = 
19
50
    (4)

Add both sides of equation (3) to both sides of equation (2), get the equation：
 A + 3B + 4C = 
187
250
    (1)
 2B = - 
19
50
    (2)
-2C = - 
19
25
    (3)
 D = 
19
100
    (4)

Multiply both sides of equation (3) by 2, get the equation：
        -4C = - 
38
25
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 A + 3B = - 
193
250
    (1)
 2B = - 
19
50
    (2)
-2C = - 
19
25
    (3)
 D = 
19
100
    (4)

Multiply both sides of equation (2) by 3
Divide both sides of equation (2) by 2, get the equation：
         3B = - 
57
100
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 A = - 
101
500
    (1)
 2B = - 
19
50
    (2)
 C = 
19
50
    (3)
 D = 
19
100
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
101
500
    (1)
 B = - 
19
100
    (2)
 C = 
19
50
    (3)
 D = 
19
100
    (4)


Therefore, the solution of the equation set is:
A = - 
101
500
B = - 
19
100
C = 
19
50
D = 
19
100


Convert the solution of the equation set to decimals:
A = -0.202000
B = -0.190000
C = 0.380000
D = 0.190000

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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