Topic awaiting preservation: Simple Math 4 Variables

x + y = 2279
w + z = 1204
x + w = 2142
y + z = 1341

I tried substitutions in all different ways, and I now know that 0 = 0. But for the life of me I can n not figure out how to solve this set of equations. Anyone have any kind of idea or a general direction I should take in solving it.


Me

As far as I can work this out, (no matter how much juggling I do)... y + z [should] = 1341

There is more than 1 error :
I have x + y + z + w = 3433

If I replace with :

x + y = 2279 and w + z = 1204 I have 3483

x + w = 2142 and y + z = 1241 I have 3383

There is some logic in it (+50 and -50) but I can't find the error. Sorry.



[This message has been edited by Moon Shadow (edited 03-05-2003).]

Are you sure there is a solution?

After playing with it for a while I get that w+z = 1104 and w+z = 1204 which is obviously wrong...

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"

I made a bit of a mistake, the number was suposed to be 1341 not 1241. I appologise for that one.


Me

x = 2279
z = 1341
y = 0
w = -137

tricky little bastard but you pretty much

lol I'm shutting up now I just solved it once Slime got the whole system thing



.:[ Never resist a perfect moment ]:.


[This message has been edited by bitdamaged (edited 03-05-2003).]

I don't believe there's enough information to solve the system, because it's impossible to isolate a single variable in an equation.

If you replace a variable in one equation with a variable whose value is solved from another equation, you will still have at least two variables in the equation. If you do this four times, you will get something in which the two variables are the same variable, and cancel out, resulting in 0=0.

The reason for this seems to be that each variable gives information about another variable (for instance, x+y=2279 means that x=2279-y and that y=2279-x), and this information occurs in a loop:

w -> x -> y -> z -> w

So you'll always make a full circle and end up with 0=0.

What does this mean? It means, in order to come up with actual numbers, you'll have to decide on a specific variable to not know what its value is. Let's pick w; we'll be able to get the values of all the other variables in terms of w:

w + z = 1204
z = 1204 - w

y + z = 1341
y + 1204-w = 1341
y = 137 + w

x + y = 2279
x + 137+w = 2279
x = 2142-w

So, there, we have x, y, and z expressed in terms of w. But that's as good as you can get. You need more information to actually get solid numerical values - the system has infinite solutions, really. For instance, one set of solutions is:

w=0
x=2142
y=137
z=1204

another set is:

w=1
x=2141
y=138
z=1203

etc.

[edit: bitdamaged has found another one of the infinite solutions. $50 to the first person to get all infinity of them! =) ]

[This message has been edited by Slime (edited 03-05-2003).]

w = 950
x = 1192
y = 1087
z = 254

[edit - one of these days, i'll read the whole thread before replying!



[This message has been edited by Dufty (edited 03-05-2003).]

[This message has been edited by Dufty (edited 03-05-2003).]

All infinity? Here goes...

w = K {K is a real number, x = 2142 - K, y = K +137, z = 1204 - K}

You could work it out for any of the 4 the same way:
x = L {L is a real number, w = L - 2142, y = L - 2005, z = L - 938}
y = M {M is a real number, w = M - 137, x = M + 2005, z = M + 1067}
z = N {N is a real number, w = 1204 - N, x = N + 938, y = N - 1067}

I know the syntax isn't exact, but it's close
Now uh, where's the $50?


-- Unoriginal Cell 693 --

That's not what I meant =)

Well, maybe you should be a bit more specific next time, lol.

edit: Flood control caught me...


-- Unoriginal Cell 693 --

wouldn't that make it a function?

couldn't you just graph it?

granted you'd need more than 3 dimentions, but that's where it gets fun!


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[This message has been edited by Petskull (edited 03-06-2003).]

Yeah, it'd be a diagonal 1-dimensional line travelling through 4 dimensions =)

Multivariable Calculus and Geometry, now we're having fun

"Now, thanks to the wonders of modern technology, this multipurpose Klein Bottle is available for a mere $80 -- cheaper than sending a spaceprobe most of the way to Mars!"
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Heh, I'm seriously thinking about getting one of those mugs

[edit: Actually that site's pretty funny in places:
"Prices slightly higher north of the Arctic circle."
"we are pleased to offer this UNCONDITIONAL GUARANTEE complete with these conditions"
"In addition, Acme's provides this exclusive LIFETIME GUARANTEE: We guarantee that you will live your entire lifetime, or double your money back"

-- Unoriginal Cell 693 --

[This message has been edited by Lord_Fukutoku (edited 03-06-2003).]

Thanks all! I came up with that same sort of circular logic. I wasn't sure if there was an actual way to solve it. I thought there might have been some trick, which slime showed me. Thanks for all the effort you put in to helping me figure this out.


Me