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Dan Hibiki
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Posted on 11-27-07 04:09:32 PM Link | Quote
You will be rewarded for your efforts!

Solve by graphing. Indicate whether each system is independent, dependent, or inconsistent:
2x - 3y = 12
3y - 2x = -12

Solve the system via the substitution method. Indicate whether each system is independent, dependent, or inconsistent:
x - 5y = 4
4x + 8y = -5

Solve the system via the addition method. Indicate whether each system is independent, dependent, or inconsistent:
x + 3(y - 1) = 11
2(x - y) + 8y = 28

Solve the system by elimination of variables:
2x + 3y - 2z = -11
3x - 2y + 3z = 7
x - 4y + 4z = 14

Solve the system by the Gauss-Jordan elimination method:
2x - y + 2z = 9
x + 3y = 5
3x + z = 9

I'll be working along side these as well, trying to come up with answers. Thanks in advance.

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Hiryuu

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Posted on 11-27-07 04:34:26 PM (last edited by Hiryuu at 11-27-07 01:34 PM) Link | Quote
Ω > U
Pre-Calc, Trig or Calc?

That's about all I can say...don't have my TI-89 on me and I'm at work so. :\

Although...for the second one...

x - 5y = 4
4x + 8y = -5

x = 4 + 5y

4(4+5y) + 8y = -5
16 + 20y + 8y = -5
28y + 16 = -5
28y = -21
y = -21/28
y = -3/4

That said... (though method might be wrong...)

x - 5(3/4) = 4
x - 15/4 (or 3 3/4) = 4
x = 31/4 (or 7 3/4)

Couldn't tell you heads from tails for system dependencies...it's been too long and I don't even know if that's right or if the method's right.


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Sine
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Posted on 11-27-07 07:01:39 PM (last edited by Kattwah at 11-27-07 04:05 PM) Link | Quote
So... anyone seen my toaster?
---------------------------------------------------- 

Solve the system by elimination of variables:

2x + 3y - 2z = -11

3x - 2y + 3z = 7

x  - 4y + 4z = 14 



First step is to make two pairs... so...



 2x + 3y - 2z = -11

-2x + 8y - 8z = -28 (third equation, multiplied through with -2)



This cancels to 11y - 10z = -39



 3x -  2y +  3z = 7

-3x + 12y - 12z = -42 (Third equation, multiplied through with -3)



This cancels to 10y - 9z = -35



Now we have a system of two equations...



11y - 10z = -39

10y -  9z = -35 



Solving this (in whatever preferred method you may choose)



-10z = -39 - 11y

z = (39/10) + (11/10)y



10y - 9((39/10) + (11/10)y) = -35

10y - 351/10 - (99/10)y = -35

10y - (99/10)y = 1/10

(1/10)y = 1/10

y = 1



11(1) - 10z = -39

11 - 10z = -39

-10z = -50

z = 5



Going back to the beginning now...



x  - 4y + 4z = 14 



x - 4(1) + 4(5) = 14

x - 4 + 20 = 14

x + 16 = 14

x = -2


So in the end, you have [x,y,z] or [-2,1,5]

(assuming my math is right)

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OoBurns
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Posted on 11-27-07 07:03:52 PM (last edited by BooUrns at 11-27-07 04:08 PM) Link | Quote
The fourth one...

2x + 3y - 2z = -11
3x - 2y + 3z = 7
x - 4y + 4z = 14

Make 2 systems of 2 equations:

2x + 3y - 2z = -11 3x - 2y + 3z = 7
x - 4y + 4z = 14 x - 4y + 4z = 14

Multiply the bottom left equation by -2, and the bottom right equation by -3, then add them up:

2x + 3y - 2z = -11 3x - 2y + 3z = 7
-2x + 8y - 8z = -28 -3x + 12y - 12z = -42
-------------------- ---------------------
11y - 10z = -39 10y - 9z = -35

Multiply the left one by -10 and the right one by 11:

-110y + 100z = 390
110y - 99z = -385
-------------------
z = 5

Substitute 5 for z in a previous equation:

11y - 10z = -39
11y - 50 = -39
y = 1

Substitute y and z in the first equation:

2x + 3y - 2z = -11
2x + 3 - 10 = -11
x = -2

It's been a while since I've done one of those. That was actually slightly entertaining. (Only slightly. I'm not doing any more.)

*BooUrns slaps Kattwah around a bit with a large calculator

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Hiryuu

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Posted on 11-27-07 08:25:01 PM Link | Quote
Ω > U
Yea that was either Trig or Pre-Calc. :\

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Sine
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Posted on 11-27-07 08:33:21 PM Link | Quote
So... anyone seen my toaster?
----------------------------------------------------

Originally posted by Hiryuu
Yea that was either Trig or Pre-Calc. :\
Technically, systems of equations is Algebra II, however you do review it in Precalc (Math Analysis)

The Gauss-Jordan elimination method I havent even heard of until today.

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Hiryuu

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Posted on 11-27-07 09:19:17 PM Link | Quote
Ω > U
That G-J crap is why I said Trig/Pre-Calc. I haven't either.

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Dan Hibiki
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Posted on 11-28-07 04:10:36 PM Link | Quote
Yeah, this is College Algebra I.
Thanks for the help so far.... I'm still working at it, and it's due tomorrow, so....
Any other help is still appreciated
*goes back to figuring this shit out*

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Hiryuu

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Posted on 11-28-07 04:40:03 PM Link | Quote
Ω > U
Huh...

Oh wait...we are at the -end- of a semester. That would make sense then.

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Skreeny
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Posted on 11-28-07 04:52:38 PM Link | Quote
Somehow, I can only seem to hear the term "Gauss-Jordan" in my head in the voice of my Calculus teacher, so I'd have to guess that's where I learned it.

Then again, that also could let it be linear algebra. Which, looking at Wikipedia, seems likely.

You do quite a bit of systems of equations in linear algebra, by the way.
Hectamatatortron
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Posted on 11-30-07 03:18:18 AM Link | Quote
Seems odd that we just covered this stuff in Differential Equations, which comes WAY after Algebra II. :/
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