How's you Algebra?

Gord.T said:
Okay, let's skip ahead a little bit then. Obviously we have some bright students here.

We can start here.

Solve:

2x + y + z = 6
x - 2y + 2z = 10
3x - y - z = 4

and show your work.

And when you get done that I have something fun for you.
Click to expand...

Solve for WHAT, Gord? You aren't giving enough information to solve these problems. Nobody really has any idea what you're after here. a + b? There's no "solution" to that.

2x + y + z = 6: Could be X =1, y = 3, z = 1. Could be X = 1, y = 2, z= 2. Could be X = 2, y = 1, z = 1. Could be more; haven't worked it.

I haven't worked through the others, but I'm sure those have multiple sets of possible answers, too.

Or, if you're just looking to solve for a single variable (such as z = 6 - y - 2x), you haven't said which.
 
Solve for x, y and z. :) re: Post #20.

And yes there is a proper answer for A + B. :)
Here's a hint: The answer IS A + B. In that order. Not B + A. Welcome to algebra. There is a protocol. haha, many people over complicate it.
(A and B are just stand in variables that can have any number. It's the equation that matters. For example we can plug in A = 3 and B = 2 and the answer is 5. blah blah.

So, A + B = A + B.

That's it. LOL.

Here's a hint...Determinants.

// The x, y and z numbers have to be the same in order to solve all three equations. It's not a puzzle, it's a method to solve a mathematical problem. :)

edit:// This link sounds pretty out there. It's really not that complicated. It's too bad they present it that way. It really is something anyone can do, even me. A lot of fancy talk there is all. It's just a little process anyone can do. Blooooffff. Anyone can learn that in one day.
 
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jcs said:
I am math guy sometimes (wrote this racing simulator, including the physics (symplectic integrator: energy accurate), tire, and fluid dynamics simulations from scratch: http://www.youtube.com/watch?v=HmVcE50RChM, http://www.youtube.com/watch?v=ydlEEVrY3qg. Tire model interacts with continuous cubic surfaces (vs. triangles)).

Solution to the simultaneous equations:
x = 2, y = -1, z = 3

(I did this the most efficient way possible. Took less than 1 second).
Click to expand...

That is correct.
I haven't done this stuff in awhile and tend to forget.

Did you use a program or something to find the answer? 1 second is pretty fast.

@Doc. haha. I had to look up Lumbricus terrestri.
 
jcs said:
Yes sir, I used Wolfram Alpha. Here is the query: http://www.wolframalpha.com/input/?i=2x+++y+++z+=+6,+x+-+2y+++2z+=+10,+3x+-+y+-+z+=+4
It's necessary to create an account and log in to see the steps (I'm most familiar with the Substitution method).
Amazing that this technology is now free- it used to be very expensive.
Click to expand...

Isn't that cool? Thanks. I signed up.

They show 4 methods to solve it. I've learned all 4 methods before but I must admit if I had to do an exam right now I'd surely fail.
That link is handy as heck.
Thanks again.

edit:// Although I didn't see Determinants there, expansion by minors, I think Cramer's Rule is the same thing. Been awhile. Very cool though.
 
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And here's the Elimination method from the site: Just for the record.



Solve the following system:
{2 x+y+z = 6 | (equation 1)
x-2 y+2 z = 10 | (equation 2)
3 x-y-z = 4 | (equation 3)

Swap equation with1:
{3 x-y-z = 4 | (equation 1)
x-2 y+2 z = 10 | (equation 2)
2 x+y+z = 6 | (equation 3)

Subtract 1/3 from :
{3 x-y-z = 4 | (equation 1)
0 x-(5 y)/3+(7 z)/3 = 26/3 | (equation 2)
2 x+y+z = 6 | (equation 3)

Multiply equation by 2:
{3 x-y-z = 4 | (equation 1)
0 x-5 y+7 z = 26 | (equation 2)
2 x+y+z = 6 | (equation 3)

Subtract 2/3 from :
{3 x-y-z = 4 | (equation 1)
0 x-5 y+7 z = 26 | (equation 2)
0 x+(5 y)/3+(5 z)/3 = 10/3 | (equation 3)

Multiply equation by 3:
{3 x-y-z = 4 | (equation 1)
0 x-5 y+7 z = 26 | (equation 2)
0 x+y+z = 2 | (equation 3)

Add 1/5 to :
{3 x-y-z = 4 | (equation 1)
0 x-5 y+7 z = 26 | (equation 2)
0 x+0 y+(12 z)/5 = 36/5 | (equation 3)

Multiply equation by 3:
{3 x-y-z = 4 | (equation 1)
0 x-5 y+7 z = 26 | (equation 2)
0 x+0 y+z = 3 | (equation 3)

Subtract 7 from :
{3 x-y-z = 4 | (equation 1)
0 x-5 y+0 z = 5 | (equation 2)
0 x+0 y+z = 3 | (equation 3)

Divide equation by 2:
{3 x-y-z = 4 | (equation 1)
0 x+y+0 z = -1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)

Add equation to2:
{3 x+0 y-z = 3 | (equation 1)
0 x+y+0 z = -1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)

Add equation to3:
{3 x+0 y+0 z = 6 | (equation 1)
0 x+y+0 z = -1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)

Divide equation by 1:
{x+0 y+0 z = 2 | (equation 1)
0 x+y+0 z = -1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)

Collect results:
Answer:
x = 2
y = -1
z = 3
 
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[chat_mode]

I used to play around with game programming a bit too as a hobby only. I really liked the vector math as it relates to rendering in software.
Specifically the dot and cross product. Those 2 are very powerful methods. They can yield so much information about the vector content. Unit vectors and such.
At any rate, this may not be an ideal video post but...what the heck. One of my favorite areas of math anyways.

[/chat_mode]

Carry on.

 
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