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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:
 35x -75y + 150z = 0    (1)
-25x + 85y + 50z = 230    (2)
 33x -43y + 10z = 0    (3)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 7, the equation can be obtained:
         25x - 
375
7
y + 
750
7
z = 0    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 35x -75y + 150z = 0    (1)
 
220
7
y + 
1100
7
z = 230    (2)
 33x -43y + 10z = 0    (3)

Multiply both sides of equation (1) by 33
Divide the two sides of equation (1) by 35, the equation can be obtained:
         33x - 
495
7
y + 
990
7
z = 0    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 35x -75y + 150z = 0    (1)
 
220
7
y + 
1100
7
z = 230    (2)
 
194
7
y - 
920
7
z = 0    (3)

Multiply both sides of equation (2) by 97
Divide the two sides of equation (2) by 110, the equation can be obtained:
         
194
7
y + 
970
7
z = 
2231
11
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 35x -75y + 150z = 0    (1)
 
220
7
y + 
1100
7
z = 230    (2)
-270z = - 
2231
11
    (3)

Multiply both sides of equation (3) by 110
Divide both sides of equation (3) by 189, get the equation：
        - 
1100
7
z = - 
22310
189
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 35x -75y + 150z = 0    (1)
 
220
7
y = 
21160
189
    (2)
-270z = - 
2231
11
    (3)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 9, get the equation：
        -150z = - 
11155
99
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 35x -75y = - 
11155
99
    (1)
 
220
7
y = 
21160
189
    (2)
-270z = - 
2231
11
    (3)

Multiply both sides of equation (2) by 105
Divide both sides of equation (2) by 44, get the equation：
         75y = 
26450
99
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 35x = 
15295
99
    (1)
 
220
7
y = 
21160
189
    (2)
 z = 
2231
2970
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
437
99
    (1)
 y = 
1058
297
    (2)
 z = 
2231
2970
    (3)


Therefore, the solution of the equation set is:
x = 
437
99
y = 
1058
297
z = 
2231
2970


Convert the solution of the equation set to decimals:
x = 4.414141
y = 3.562290
z = 0.751178

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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