# Strange simultaneous eqution problem?

1. Oct 7, 2007

### smileandbehappy

I have a few of these to do so would appretiate if someone could explain this to me as i am stumped.

Find in terms of k a solution to the equations,

x+y+kz=4
x-2y-z=1
kx+7y+5z=10

For what values of k is this solution not valid?

Man thanks in advance for any help given.

2. Oct 7, 2007

### HallsofIvy

Staff Emeritus
Doesn't look strange to me, looks like a fairly typical problem.

How you would do it depends upon how you want to solve simultaneous linear equations! Some people might eliminate one variable at a time. If you do it that way, you will want to keep track divisions by a quantity involving k. For what values of k would you be dividing by 0? Others might set it up as a matrix equation and find the inverse of the coefficient matrix. For what values of k does that matrix not have an inverse? Still others might use Cayley's method: each solution is a fraction in which the denominator is the determinant formed by the coefficients. For what values of k is that determinant equal to 0? Of course, a little reflection will show you that all of those methods are really the same thing!

3. Oct 7, 2007

### smileandbehappy

OK then. Will you show me how to do the elimination method?

4. Oct 7, 2007

### symbolipoint

Use elementary row operations, at least to put into, ?triangular form? What course are you studying? If linear algebra, then the system should be easy to solve. You could read about one or two methods from an intermediate algebra book just as well.

5. Oct 8, 2007

### hotvette

This link takes you through a 3 x 3 example of elimination:

http://en.wikipedia.org/wiki/Gaussian_elimination

This problem is quite straightforward. There are two values of z (both whole numbers) that result in no solution. The solution to a quadratic equation is involved.