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

  • MHB
  • Thread starter mrk79blr
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In summary: K/10*276+10K/10*340for y, the answer is y = 13K/10*329-1K/10*276-2K/10*340for z, the answer is z = 13K/10*329-1K/10*276-2K/10*340In summary, we have a system of three linear equations in three variables: 329x / (329x + 276y + 340z + 332Any) =0.5, 276y / (329x + 276y + 340z + 332Any) =0.1, and 340z / (329x +
  • #1
mrk79blr
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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
 
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  • #2
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.
 
  • #3
Re: How to solve this rquation

DavidCampen said:
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
 
  • #4
Re: How to solve this rquation

It looks linear to me. Why do you think that it is non-linear?
 
  • #5
Re: How to solve this rquation

mrk79blr said:
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
 
Last edited:
  • #6
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.

- - - Updated - - -

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

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

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

How do I know what method to use to solve an equation?

The method used to solve an equation depends on the type of equation and the form it is in. For linear equations, the most common method is to isolate the variable on one side of the equation. For quadratic equations, factoring or using the quadratic formula is often used. It is important to familiarize yourself with different methods and practice solving equations to determine which method works best for each type of equation.

Can I use a calculator to solve equations?

Calculators can be useful in solving equations, especially for more complex equations with multiple variables. However, it is important to understand the steps involved in solving an equation by hand before relying solely on a calculator. It is also important to check your answers by plugging them back into the original equation.

What are some common mistakes to avoid when solving equations?

One common mistake when solving equations is forgetting to perform the same operation on both sides of the equation. This leads to an incorrect solution. Another mistake is not distributing a negative sign or not simplifying fractions. It is important to go through each step carefully and double-check your work.

Is it possible to have more than one solution to an equation?

Yes, some equations may have more than one solution. These are called "solutions" or "roots" of the equation. For example, a quadratic equation can have two solutions, and a cubic equation can have three solutions. It is important to check your solutions by plugging them back into the original equation to make sure they are valid.

How do I check if my solution is correct?

The best way to check if your solution is correct is to plug it back into the original equation and see if it satisfies the equation. If the solution makes the equation true, then it is a valid solution. Another method is to graph the equation and see if the solution(s) intersect with the graph at the given point(s).

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