Can This System of Equations Be Solved for Variables x, y, z, and Any?

[mrk79blr]

329x / (329x + 276y + 340z + 332Any) =0.5

276y / (329x + 276y + 340z + 332Any) =0.1

340z / (329x + 276y + 340z + 332Any) =0.2

We need to figure x,y,z and Any value. "Any" don't have any equation, so it can be any value.

Anyone can help me how to solve the above problem?

Thanks

 

[DavidCampen]

Re: How to solve this rquation

Don't worry about the Any, for the moment take Any to be zero. Then you have 3 linear equations in 3 variables and I presume that you are studying solving systems of linear equations.

 

[mrk79blr]

Re: How to solve this rquation

Don't worry about the Any, for the moment take Any to be zero. Then you have 3 linear equations in 3 variables and I presume that you are studying solving systems of linear equations.

It is non linear equation

 

[DavidCampen]

Re: How to solve this rquation

It looks linear to me. Why do you think that it is non-linear?

 

[mrk79blr]

Re: How to solve this rquation

It is non linear equation

Sorry it is linear equation only, But when i convert all the variables are coming as zero. Plz advice what i am doing wrong.

I consider Any as zero. So I am ignoring the same from the above equation.

If I simply the equation I will get following result
equation 1
329x / (329x + 276y + 340z) =0.5
329x=0.5 * (329x + 276y + 340z)
329x=164.5x + 138y + 170z
329x-164.5x-138y-170z=0
164.5x-138y-170z=0

equation 2
276y / (329x + 276y + 340z) =0.1
276y= 32.9x+27.6y+34.0z
-32.9x+248.4y-34.0z=0

equation 3
340z / (329x + 276y + 340z) =0.2
340z=65.8x+55.2y+68z
-65.8x-55.2y+272z=0

After simplify the 3 equation i will get 3 equations as follow
164.5x-138y-170z=0
-32.9x+248.4y-34.0z=0
-65.8x-55.2y+272z=0

Now x,y,z value is zero It will solve the above 3 equations. But If i set the values as zero in the actual equation it will not solve

329x / (329x + 276y + 340z) =0.5
276y / (329x + 276y + 340z) =0.1
340z / (329x + 276y + 340z) =0.2

So I am sure i have made some mistake. Please advice me.

Thanks

 

[DavidCampen]

Re: How to solve this rquation

So you can solve the given system of equations? I have. What is the answer?

Are you saying that you want to design an algorithm to solve any system of linear equations? You can do this by manipulating matrices.

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Instead of setting Any to zero, perform a substitution. Substitute K for 332Any.

for x, the answer is x = -45K/10*329