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:
 36A + 8D = 1000    (1)
 34B + 7D = 1000    (2)
 24C + 5D = 1000    (3)
 7A + 7B + 7C + 19D = 1000    (4)
Question solving process:

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 36, the equation can be obtained:
         7A + 
14
9
D = 
1750
9
    (5)
, then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
 36A + 8D = 1000    (1)
 34B + 7D = 1000    (2)
 24C + 5D = 1000    (3)
 7B + 7C + 
157
9
D = 
7250
9
    (4)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 34, the equation can be obtained:
         7B + 
49
34
D = 
3500
17
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 36A + 8D = 1000    (1)
 34B + 7D = 1000    (2)
 24C + 5D = 1000    (3)
 7C + 
4897
306
D = 
91750
153
    (4)

Multiply both sides of equation (3) by 7
Divide the two sides of equation (3) by 24, the equation can be obtained:
         7C + 
35
24
D = 
875
3
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 36A + 8D = 1000    (1)
 34B + 7D = 1000    (2)
 24C + 5D = 1000    (3)
 
17803
1224
D = 
47125
153
    (4)

Multiply both sides of equation (4) by 6120
Divide both sides of equation (4) by 17803, get the equation:
         
4685
937
D = 
1885000
17803
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
 36A + 8D = 1000    (1)
 34B + 7D = 1000    (2)
 24C = 
15918000
17803
    (3)
 
17803
1224
D = 
47125
153
    (4)

Multiply both sides of equation (4) by 8568
Divide both sides of equation (4) by 17803, get the equation:
         
6559
937
D = 
2639000
17803
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 36A + 8D = 1000    (1)
 34B = 
15164000
17803
    (2)
 24C = 
15918000
17803
    (3)
 
17803
1224
D = 
47125
153
    (4)

Multiply both sides of equation (4) by 9792
Divide both sides of equation (4) by 17803, get the equation:
         
7496
937
D = 
3016000
17803
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
 36A = 
14787000
17803
    (1)
 34B = 
15164000
17803
    (2)
 24C = 
15918000
17803
    (3)
 
17803
1224
D = 
47125
153
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
410750
17803
    (1)
 B = 
446000
17803
    (2)
 C = 
663250
17803
    (3)
 D = 
377000
17803
    (4)


Therefore, the solution of the equation set is:
A = 
410750
17803
B = 
446000
17803
C = 
663250
17803
D = 
377000
17803


Convert the solution of the equation set to decimals:
A = 23.071954
B = 25.051958
C = 37.254957
D = 21.176206

解方程组的详细方法请参阅:《多元一次方程组的解法》







  New addition:Lenders ToolBox module(Specific location:Math OP > Lenders ToolBox ),welcome。