System involving nonlinear equations.

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Discussion Overview

The discussion revolves around approaches to obtaining the inverse of a system of nonlinear equations, specifically focusing on the equations 3x² - 2y = i and x + y = j. Participants explore methods for expressing x and y in terms of i and j, while clarifying that this is not a homework problem.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant suggests substituting y = j - x into the first equation to simplify the system.
  • Another participant provides a solution for x as x = ±(1/3)(√(6j + 3i + 1) - 1) after substitution.
  • There is a mention of difficulties with similar problems, indicating a personal struggle with the concepts involved.
  • A later post asserts that all workable nonlinear equations can be reduced to a system of linear equations, though this claim lacks further elaboration.
  • Another participant makes a vague statement about the relationship between linear equations and reality, without providing specific details or context.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints on the approach to solving the nonlinear equations, and there is no consensus on the best method or the validity of the claims regarding linear equations.

Contextual Notes

Some assumptions about the nature of the equations and their solutions are not explicitly stated, and the discussion does not resolve the complexities involved in nonlinear systems.

D.K
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What is the best approach for obtaining the inverse of a system of equations involving nonlinear equations?
Say:
3x^2 - 2y = i
x + y = j
Solving for x and y in terms of i and j?
Note: This is not a homework problem, just a general question.
 
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D.K said:
What is the best approach for obtaining the inverse of a system of equations involving nonlinear equations?
Say:
3x^2 - 2y = i
x + y = j
Solving for x and y in terms of i and j?
Note: This is not a homework problem, just a general question.

Here, I would say y=j-x then substitute that in for y.

3x^2 - 2(j-x) = i

Solve for x...

x = \pm \frac{1}{3} \left(\sqrt{6 j+3 i+1}-1\right)

Then, knowing what x is, substitute x in the second equation to express y in terms of i and j.
 
Char. Limit said:
Here, I would say y=j-x then substitute that in for y.

3x^2 - 2(j-x) = i

Solve for x...

x = \pm \frac{1}{3} \left(\sqrt{6 j+3 i+1}-1\right)

Then, knowing what x is, substitute x in the second equation to express y in terms of i and j.

Thanks a lot. For some reason, I have always had difficulty with simple things like these!
 
There are no workable non lin equations that aren't reduced to a sum lin equations

blah blah blah
 
The real sht is identifying lin equations to reality
 

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