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 + B = 79060    (1)
 C + D = 10924    (2)
377
400
C + 
17
400
D = 0    (3)
17
400
B + 
17
400
D = 0    (4)
Question solving process:

交After the exchange of equation (2) and equation (4), the equation system becomes:
 A + B = 79060    (1)
17
400
B + 
17
400
D = 0    (2)
377
400
C + 
17
400
D = 0    (3)
 C + D = 10924    (4)

Multiply both sides of equation (3) by 400
Divide the two sides of equation (3) by 377, the equation can be obtained:
        -1C + 
17
377
D = 0    (5)
, then add the two sides of equation (5) to both sides of equation (4), the equations are reduced to:
 A + B = 79060    (1)
17
400
B + 
17
400
D = 0    (2)
377
400
C + 
17
400
D = 0    (3)
 
394
377
D = 10924    (4)

Multiply both sides of equation (4) by 6409
Divide both sides of equation (4) by 157600, get the equation:
         
3349
78800
D = 
17502979
39400
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), get the equation:
 A + B = 79060    (1)
17
400
B + 
17
400
D = 0    (2)
377
400
C = 
17502979
39400
    (3)
 
394
377
D = 10924    (4)

Multiply both sides of equation (4) by 6409
Divide both sides of equation (4) by 157600, get the equation:
         
3349
78800
D = 
17502979
39400
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
 A + B = 79060    (1)
17
400
B = 
17502979
39400
    (2)
377
400
C = 
17502979
39400
    (3)
 
394
377
D = 10924    (4)

Multiply both sides of equation (2) by 400
Divide both sides of equation (2) by 17, get the equation:
        -1B = 
2059174
197
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 A = 
13515646
197
    (1)
17
400
B = 
17502979
39400
    (2)
 C = 
92854
197
    (3)
 D = 
2059174
197
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
13515646
197
    (1)
 B = 
2059174
197
    (2)
 C = 
92854
197
    (3)
 D = 
2059174
197
    (4)


Therefore, the solution of the equation set is:
A = 
13515646
197
B = 
2059174
197
C = 
92854
197
D = 
2059174
197


Convert the solution of the equation set to decimals:
A = 68607.340102
B = 10452.659898
C = 471.340102
D = 10452.659898

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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