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:
 203x + 39y + 7z = 1    (1)
 320x + 52y + 8z = 1    (2)
 671x + 91y + 11z = 1    (3)
Question solving process:

Multiply both sides of equation (1) by 320
Divide the two sides of equation (1) by 203, the equation can be obtained:
         320x + 
12480
203
y + 
320
29
z = 
320
203
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 203x + 39y + 7z = 1    (1)
1924
203
y 
88
29
z = 
117
203
    (2)
 671x + 91y + 11z = 1    (3)

Multiply both sides of equation (1) by 671
Divide the two sides of equation (1) by 203, the equation can be obtained:
         671x + 
26169
203
y + 
671
29
z = 
671
203
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 203x + 39y + 7z = 1    (1)
1924
203
y 
88
29
z = 
117
203
    (2)
7696
203
y 
352
29
z = 
468
203
    (3)

Multiply both sides of equation (2) by 4, the equation can be obtained:
        
7696
203
y 
352
29
z = 
468
203
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 203x + 39y + 7z = 1    (1)
1924
203
y 
88
29
z = 
117
203
    (2)
0 = 0    (3)

Multiply both sides of equation (2) by 609
Divide both sides of equation (2) by 148, get the equation:
        -39y 
462
37
z = 
351
148
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation:
 203x 
203
37
z = 
203
148
    (1)
1924
203
y 
88
29
z = 
117
203
    (2)
0 = 0    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x 
1
37
z = 
1
148
    (1)
 y + 
154
481
z = 
117
1924
    (2)
0 = 0    (3)


Therefore, the solution of the equation set is:
x = 
1
148
 + 
1
37
z
y = 
117
1924
 - 
154
481
z


Convert the solution of the equation set to decimals:
x = -0.006757 + 
1
37
z
y = 0.060811 - 
154
481
z

Where:  z are arbitrary constants.
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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