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:
 60A + 8D = 75    (1)
 36B + 6D = 65    (2)
 35C + 7D = 40    (3)
 8A + 8B + 8C + 32D = 89    (4)
Question solving process:

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 15, the equation can be obtained:
         8A + 
16
15
D = 10    (5)
, then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
 60A + 8D = 75    (1)
 36B + 6D = 65    (2)
 35C + 7D = 40    (3)
 8B + 8C + 
464
15
D = 79    (4)

Multiply both sides of equation (2) by 2
Divide the two sides of equation (2) by 9, the equation can be obtained:
         8B + 
4
3
D = 
130
9
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 60A + 8D = 75    (1)
 36B + 6D = 65    (2)
 35C + 7D = 40    (3)
 8C + 
148
5
D = 
581
9
    (4)

Multiply both sides of equation (3) by 8
Divide the two sides of equation (3) by 35, the equation can be obtained:
         8C + 
8
5
D = 
64
7
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 60A + 8D = 75    (1)
 36B + 6D = 65    (2)
 35C + 7D = 40    (3)
 28D = 
3491
63
    (4)

Divide both sides of equation (4) by 4, get the equation:
         7D = 
3491
252
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
 60A + 8D = 75    (1)
 36B + 6D = 65    (2)
 35C = 
6589
252
    (3)
 28D = 
3491
63
    (4)

Multiply both sides of equation (4) by 3
Divide both sides of equation (4) by 14, get the equation:
         6D = 
3491
294
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 60A + 8D = 75    (1)
 36B = 
15619
294
    (2)
 35C = 
6589
252
    (3)
 28D = 
3491
63
    (4)

Multiply both sides of equation (4) by 2
Divide both sides of equation (4) by 7, get the equation:
         8D = 
6982
441
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
 60A = 
26093
441
    (1)
 36B = 
15619
294
    (2)
 35C = 
6589
252
    (3)
 28D = 
3491
63
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
26093
26460
    (1)
 B = 
15619
10584
    (2)
 C = 
6589
8820
    (3)
 D = 
3491
1764
    (4)


Therefore, the solution of the equation set is:
A = 
26093
26460
B = 
15619
10584
C = 
6589
8820
D = 
3491
1764


Convert the solution of the equation set to decimals:
A = 0.986130
B = 1.475718
C = 0.747052
D = 1.979025

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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