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

[judahs_lion]

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

Attached

 

[LCKurtz]

What in the world is an expression like

$$\frac{\binom{x+ky=1}{kx+y=1}}{y}$$

supposed to mean?

Do you know Cramer's rule? Can you find a k that makes the equations dependent? Inconsistent?

 

[jrlaguna]

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.

 

[Mark44]

The problem statement is shown as

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."