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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:
 33x -43y + 10z = 0    (1)
-5x + 17y + 10z = 40    (2)
 x + y + 10z = 20    (3)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 33, the equation can be obtained:
         5x - 
215
33
y + 
50
33
z = 0    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 33x -43y + 10z = 0    (1)
 
346
33
y + 
380
33
z = 40    (2)
 x + y + 10z = 20    (3)

Divide the two sides of equation (1) by 33, the equation can be obtained:
         x - 
43
33
y + 
10
33
z = 0    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 33x -43y + 10z = 0    (1)
 
346
33
y + 
380
33
z = 40    (2)
 
76
33
y + 
320
33
z = 20    (3)

Multiply both sides of equation (2) by 38
Divide the two sides of equation (2) by 173, the equation can be obtained:
         
13148
5709
y + 
14440
5709
z = 
1520
173
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 33x -43y + 10z = 0    (1)
 
346
33
y + 
380
33
z = 40    (2)
 
1240
173
z = 
1940
173
    (3)

Multiply both sides of equation (3) by 3287
Divide both sides of equation (3) by 2046, get the equation：
         
65740
5709
z = 
18430
1023
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 33x -43y + 10z = 0    (1)
 
346
33
y = 
22490
1023
    (2)
 
1240
173
z = 
1940
173
    (3)

Multiply both sides of equation (3) by 173
Divide both sides of equation (3) by 124, get the equation：
         
1730
173
z = 
83905
5363
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 33x -43y = - 
83905
5363
    (1)
 
346
33
y = 
22490
1023
    (2)
 
1240
173
z = 
1940
173
    (3)

Multiply both sides of equation (2) by 1419
Divide both sides of equation (2) by 346, get the equation：
         
7439
173
y = 
483535
5363
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 33x = 
399630
5363
    (1)
 
346
33
y = 
22490
1023
    (2)
 z = 
16781
10726
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
12110
5363
    (1)
 y = 
11245
5363
    (2)
 z = 
16781
10726
    (3)


Therefore, the solution of the equation set is:
x = 
12110
5363
y = 
11245
5363
z = 
16781
10726


Convert the solution of the equation set to decimals:
x = 2.258065
y = 2.096774
z = 1.564516

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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