Solving a system of equations vs. doing dishes

I was getting ready to face the 'challenge' of a kitchen counter filled with dirty dishes, when I started thinking about the task ahead and how it compares to problem solving in math.

Then I found a funny little comparison between washing dishes and solving a system of linear equations.

You see, when you tackle that counter, you first need to organize things and move dishes around so you can see your kitchen sink again.

Just like if you have, say for example, these equations:

2x - 4y + 3x = 2z - 4/5x + 67y
4y - 0.3x - 0.98x + 34z = 5z + 90x - 0.2y
z - 2/3z + 3y -0.3x = 7y - 5/6z + 90x - 45x
Just looks messy and almost discouraging! x's and y's and z's all over the place!

But then you start moving things around (moving x's, y's, and z's all to the left side), and making piles of plates, putting pots in one corner, containers in another pile (combining x's, y's, and z's), making the other side of the counter empty (zero) - and voila - it looks much simpler now. I feel I can manage the task now!

5 4/5x - 71y - 2z = 0
- 91.28x + 4.2y + 29z = 0
-45.3x - 4y + 1 1/6z = 0
Then it's time to really start working (multiplying and dividing). Actually there are several methods, did you know? Some people do glasses first, some people start with silverware (you can use elimination method, or substitution method - or even Cramer's rule). But they all produce the same end result.

Over time, the task becomes routine (even boring) and you can just about do it without much thinking.

And, if you really just feel lazy, you can always leave dishes for tomorrow, or train a child in your family to do them (this system of equations is left for homework for the reader :).

Disclaimer: I am not guaranteeing there is a solution. Some dishes just resist washing.
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