Mathematics
         
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Multivariate equation
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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:
 27x + 
21
2
y = - 
814
5
    (1)
 
21
2
x + 7y = 
1329
10
    (2)
Question solving process:

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 18, the equation can be obtained:
         
21
2
x + 
49
12
y = - 
2849
45
    (3)
, then subtract both sides of equation (3) from both sides of equation (2), the equations are reduced to:
 27x + 
21
2
y = - 
814
5
    (1)
 
35
12
y = 
17659
90
    (2)

Multiply both sides of equation (2) by 18
Divide both sides of equation (2) by 5, get the equation：
         
21
2
y = 
17659
25
    (4)
, then subtract both sides of equation (4) from both sides of equation (1), get the equation：
 27x = - 
21729
25
    (1)
 
35
12
y = 
17659
90
    (2)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
7243
225
    (1)
 y = 
35318
525
    (2)


Therefore, the solution of the equation set is:
x = - 
7243
225
y = 
35318
525


Convert the solution of the equation set to decimals:
x = -32.191111
y = 67.272381

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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