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

1. Apr 8, 2010

### judahs_lion

1. The problem statement, all variables and given/known data

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

2. Relevant equations

x + ky = 1
kx + y =1

3. The attempt at a solution

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2. Apr 8, 2010

### 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?

3. Apr 9, 2010

### 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.

4. Apr 9, 2010

### Staff: Mentor

The problem statement is shown as
It makes more sense as "Find values of k for which the system of equations has no solution, many solutions, a unique solution."