# Need help with systems of linear equations!!



## Flame Sixtyone (Aug 27, 2009)

so there's a 2X2 system of linear equations

x+2y=3 
2x-y=-4

The question asks: 
- Examine the constants in the two individual equations and describe any patterns.
- Solve the system and show a graphical representation. What is the significance of the solution?
- Create and solve a few more systems similar to this. Comment on your solutions.
- Make a conjecture regarding this type of 2X2 system and prove it.

I can easily solve the system and graph it. x=-1 and y=2. But i'm having trouble with identifying any patterns in the constants.
The constants for the first equation are [1 2 3]. and for the second equation they are [2 -1 4]. Can anyone help me find a pattern in it?
I also need help find a conjecture for this type of a system


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## lostinlife (Jun 2, 2010)

I think they want you to look at the pattern across each equation, so:
1 , 2, 3 is 1 + 1 = 2 then 2 + 1 = 3
2, -1, -4 is 2 - 3 = -1 then -1 - 3 = -4

That is, the first equation decreases by a constant number between constants (+1 between terms) and the second equation decreases by a constant number between constants (-3 between terms).

From this, write out other examples of systems of equations that have one equation with constants that increase by a constant number between terms and the other equation with constants that decrease by a constant number between terms. 

I don't have much experience with conjectures/proofs but this might be able to help you get started.


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## geeknick (Nov 11, 2011)

linear equation with 3 variables?

When asked to solve: 
a + b = 3
-b + c = 3
a + 2c =10......how do you solve for a variable if you cannot solve for the same variable (using elimination) for the 1st and 2nd and 2nd and 3rd equations? Or in other words, how would you solve this using elimination?


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## cavemanslaststand (Jan 6, 2011)

What the aboves said, but also:

They are simply asking you to say the two lines are perpendicular based on coefficients.

Sytems that are orthogonal simply have

m1 = - 1/m2 
A1 / B1 = - B2 / A2

1 /2 = - (-1/ 2)

The slope of one is the negative inverse of the slope of the other.

If that's too confusing:

A1 * A2 = - B1 * B2

where A1 and B1 and A2 and B2 are coefficients of the equations respectively.

If there's any doubt, rewrite both as y = m x + b

and m1 * m2 = -1

Not sure what level of math this is (Algebra or Linear Algebra), but there's a concise relationship with matrix coefficients in linear algebra that describes orthogonality:

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


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## seafolly (Jun 17, 2010)

Well I'm officially second guessing my selection of Linear Algebra next semester. I don't recall touching that in high school but perhaps it's just been too long!

Edit: Oh wait. Yes I remember that. Still. The question read as Chinese for far too long there!


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## cavemanslaststand (Jan 6, 2011)

seafolly said:


> Well I'm officially second guessing my selection of Linear Algebra next semester. I don't recall touching that in high school but perhaps it's just been too long!
> 
> Edit: Oh wait. Yes I remember that. Still. The question read as Chinese for far too long there!


Stick with linear algebra (partly since it's required for your field?).

Linear algebra formal defintions are a little confusing if not scary, but people will always say it's easier than calc because actual worked examples are more of book-keeping of matrices than some of really ugly integrals in calc.

It will be more practical exercises and less abstract than wiki articles describing it.


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## seafolly (Jun 17, 2010)

cavemanslaststand said:


> Stick with linear algebra (partly since it's required for your field?).
> 
> Linear algebra formal defintions are a little confusing if not scary, but people will always say it's easier than calc because actual worked examples are more of book-keeping of matrices than some of really ugly integrals in calc.
> 
> It will be more practical exercises and less abstract than wiki articles describing it.


Interesting! I did extremely well in calculus but I've heard one's brain is geared for one or the other. It's not actually required for my degree, I just thought I'd take another math course instead of having to do more botany (dry much?). Stats is the only math course required beyond calculus for me.


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## Flame Sixtyone (Aug 27, 2009)

I hope you all realize that thread was created one year ago! Although I do appreciate the help


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