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

  • Context: MHB 
  • Thread starter Thread starter mrk79blr
  • Start date Start date
Click For Summary
SUMMARY

The discussion revolves around solving a system of linear equations involving variables x, y, z, and an arbitrary value termed "Any." The equations are derived from proportions of x, y, and z, leading to three linear equations: 164.5x - 138y - 170z = 0, -32.9x + 248.4y - 34.0z = 0, and -65.8x - 55.2y + 272z = 0. A participant suggests substituting "Any" with a variable K for simplification, leading to a solution for x as x = -45K/10*329. The consensus confirms that the equations are linear, despite initial confusion regarding their nature.

PREREQUISITES
  • Understanding of linear equations and systems of equations
  • Familiarity with algebraic manipulation and simplification techniques
  • Knowledge of substitution methods in solving equations
  • Basic understanding of matrix operations for algorithm design
NEXT STEPS
  • Study methods for solving systems of linear equations using substitution
  • Learn about matrix manipulation techniques for solving linear equations
  • Explore the implications of introducing arbitrary constants in equations
  • Investigate algorithms for solving any system of linear equations
USEFUL FOR

Mathematics students, educators, and anyone interested in solving linear equations or developing algorithms for mathematical problem-solving.

mrk79blr
Messages
3
Reaction score
0
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
 
Physics news on Phys.org
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.
 
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
 
Re: How to solve this rquation

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

Similar threads

Undergrad Did I figure-out z-translation of 2D-coordinates correctly?
  • · Replies 4 ·
Replies
4
Views
3K
MHB Solving System of Equations: xy, yz, zx
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solve System of Equations: Find x, y, z & l1, l2, l3
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Using an array to solve a system of equations
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Proof for subgroup -- How prove it is a subgroup of Z^m?
  • · Replies 11 ·
Replies
11
Views
3K
High School Parametric Representation of Lines
  • · Replies 13 ·
Replies
13
Views
3K
High School Solving for the Nth divergence in any coordinate system
  • · Replies 41 ·
2
Replies
41
Views
4K
MHB Mason's question via Facebook about solving a system of equations (2)
  • · Replies 1 ·
Replies
1
Views
10K
MHB Solving Systems of Six Equations with Nine Variables
  • · Replies 1 ·
Replies
1
Views
2K
MHB Mason's question via Facebook about solving a system of equations
  • · Replies 1 ·
Replies
1
Views
11K