Solving Systems of Equations

[Amaton]

I'm doing work for math class (high school level), and we're currently on linear systems of equations.

Simple linear systems like:

[math]x-3y-z=-1[/math]
[math]2x+2y+2z=0[/math]
[math]3x+y+3z=2[/math]

...as taken from my text.

Some of several methods we're expected to use are elementary substitution and elimination (there are more efficient ways, but these are the focus for now).

What's peculiar is that for some of the problems, it takes me 3 or 4 attempts to finally get a working answer when using these methods. I'm not sure why, but I often derive an answer which only solves one or two of the equations, rather than all the equations in the system.

This is pretty strange, since whenever this happens, I can never pick out what I did wrong in the algebra. After the first one flops, I go at it again and derive a different answer. This time, however, it solves only some of the equations, just in a different combination/order... still not the entire system.

 

Some of the problems take me quite a while to get a "global" solution, as I like to think of them in contrast to "local" ones which only satisfy part of the system.

 

Why does this happen? And how can I work around the issue (still using these methods)?

[John]

Can you provide an example of a problem you've attempted to solve that gave you trouble, along with what steps you took?

[ajb]

Why does this happen? And how can I work around the issue (still using these methods)?

As John points out, without a clear example of your work it is hard to comment. However, I will say that solving systems of equations has many steps that allow for elementary mistakes. The ideas can be simple, but mistakes creep in while doing the computations. Or at least, that is my experience.

[Amaton]

Of course. I'll look through the work and see if I could a good example...

[Amaton]

Sorry for my absence. In the while, I've gone through matrix solutions and other methods, but I don't feel for recalling those troublesome problems. Thanks anyway.

[ajb]

Sorry for my absence. In the while, I've gone through matrix solutions and other methods, but I don't feel for recalling those troublesome problems. :doh:Thanks anyway.

Using matrices, either via Gaussian elimination or Cramer's rule is a good way to tackle systems of equations like the one you mention earlier. These methods are far better than substitution or elimination, unless the system of equations is particularly nice.