Find values of K for which k has no solution, many solutions a unique solution

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Homework Help Overview

The discussion revolves around finding values of K in a system of linear equations represented by x + ky = 1 and kx + y = 1, specifically focusing on conditions that lead to no solutions, many solutions, or a unique solution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods to analyze the system, including solving for x and y as functions of k and checking for inconsistencies, as well as using graphical interpretations of the equations to determine the nature of the solutions.

Discussion Status

There are multiple approaches being explored, including algebraic and graphical methods. Some participants question the clarity of the problem statement and suggest a rephrasing for better understanding. Guidance on using Cramer's rule and identifying dependent or inconsistent equations has been mentioned.

Contextual Notes

There is a noted ambiguity in the original problem statement, which some participants feel could lead to confusion regarding the interpretation of k and the nature of the solutions.

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Homework Statement



Find values of K for which k has no solution, many solutions a unique solution

Homework Equations



x + ky = 1
kx + y =1


The Attempt at a Solution



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What in the world is an expression like

[tex]\frac{\binom{x+ky=1}{kx+y=1}}{y}[/tex]

supposed to mean?

Do you know Cramer's rule? Can you find a k that makes the equations dependent? Inconsistent?
 
Method I: Try to solve the system for x and y as a function of k. Now check for which values of k the solution makes no sense (for example, if you have to divide by 0). Those are the values for which the system is inconsistent, so no solutions.

Method II: graphical method. The two equations give two lines in the plane. If the cut at a point, the system is fine. If they're the same line, the system has many solutions. If they're parallel, the system has no solutions.
 
The problem statement is shown as
judahs_lion said:
Find values of K for which k has no solution, many solutions a unique solution
It makes more sense as "Find values of k for which the system of equations has no solution, many solutions, a unique solution."
 

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