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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:
 40x -20y - 
1
2
z = -7    (1)
-20x + 61y + 
1
2
z = 91    (2)
 20x + z = 0    (3)
Question solving process:

Divide the two sides of equation (1) by 2, the equation can be obtained:
         20x -10y - 
1
4
z = - 
7
2
    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 40x -20y - 
1
2
z = -7    (1)
 51y + 
1
4
z = 
175
2
    (2)
 20x + z = 0    (3)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         20x -10y - 
1
4
z = - 
7
2
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 40x -20y - 
1
2
z = -7    (1)
 51y + 
1
4
z = 
175
2
    (2)
 10y + 
5
4
z = 
7
2
    (3)

Multiply both sides of equation (2) by 10
Divide the two sides of equation (2) by 51, the equation can be obtained:
         10y + 
5
102
z = 
875
51
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 40x -20y - 
1
2
z = -7    (1)
 51y + 
1
4
z = 
175
2
    (2)
 
245
204
z = - 
1393
102
    (3)

Multiply both sides of equation (3) by 51
Divide both sides of equation (3) by 245, get the equation：
         
1
4
z = - 
199
70
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 40x -20y - 
1
2
z = -7    (1)
 51y = 
3162
35
    (2)
 
245
204
z = - 
1393
102
    (3)

Multiply both sides of equation (3) by 102
Divide both sides of equation (3) by 245, get the equation：
         
1
2
z = - 
199
35
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 40x -20y = - 
444
35
    (1)
 51y = 
3162
35
    (2)
 
245
204
z = - 
1393
102
    (3)

Multiply both sides of equation (2) by 20
Divide both sides of equation (2) by 51, get the equation：
         20y = 
248
7
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 40x = 
796
35
    (1)
 51y = 
3162
35
    (2)
 z = - 
398
35
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
199
350
    (1)
 y = 
62
35
    (2)
 z = - 
398
35
    (3)


Therefore, the solution of the equation set is:
x = 
199
350
y = 
62
35
z = - 
398
35


Convert the solution of the equation set to decimals:
x = 0.568571
y = 1.771429
z = -11.371429

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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