ALGEBRA!!!

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Postby Pookie » Mon Oct 31, 2005 4:18 pm

Miranda wrote:Umm, i know, nothing, i guess...
I missed the term we started algebra, then came to a different school where they were further on at it than i ever was so i havent a clue, here's a question, and how i worked on it:

xsquared + ysquared = 10
2x+y=-5
2x=-5+y
2x-+5=-y
-2x+-5=y
y=-2x+-5
xsquared + (-2x+-5)squared = 10
im stuck


Hang on which part is the question and which part is your workings out?

I am presuming the question is, find x and y given that

x^2+y^2=10 and 2x+y=5 ?

Square 2x+y =5

So you get 4x^2+y^2=25

So you now have x^2+y^2=10 and 4x^2+y^2=25 . These are called simultaneous equations and to find the answer you subtract one from the other.

Now you can write it as a straightforward substitution

4x^2+y^2=25
minus x^2+y^2=10
___________________
3x^2=15

therefore x=sqrt 5 and y=sqrt 5


or you might like this way better

rearrange the equations so you have zero on the right of each and put them equal to each other

4x^2+y^2-25=0
x^2+y^2-10=0

therefore

4x^2+y^2-25=x^2+y^2-10

and solve from there
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Algebra

Postby pinkparrot » Mon Oct 31, 2005 6:31 pm

I don't know what you're on about, Pookie. I did this:

O.K, Miranda, take a look.

2x + y = 5
5 = 2x + y
5 - 2x = y
5 - y = 2x

2x = 5 - y
y = 5 - 2x
(To clarify the equation)To have the "x" or "y" = whatever

Then dealt with the xsquared + ysquared = 10

xsquared + ysquared = 10

Then checked a few numbers squared:
1squared = 1
2squared = 4
3squared = 9

Then I got it:

1squared + 3squared = 10 1 + 9 = 10

But I didn't know which way round the answers were, so I tried x being 1 and y being 3. I tried it with the equation.


So 2x = 5 - y would be (2 x 1) = 5 - 3
i.e 2 = 2, which is right.

So x=1 and y=3. This is your final answer.

This is solving the equation (I think I did it right), by trial and improvement which is not a good idea in the exam. I did it this way because I would want you to understand what's going on. The principle is substitution, which Pookie was on about.
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Re: Algebra

Postby Pookie » Mon Oct 31, 2005 9:10 pm

pinkparrot wrote:I don't know what you're on about, Pookie.


Yes ignore me! :oops: I was making it into something it isn't, something which I normally do. Anyone else have the problem of thinking they are reading something which they aren't?

Question Find x and y given that

x^2+y^2=10 and 2x+y=5 ?

y = 5 -2x

Substitute in

x^2 + (5-2x)^2 =10
x^2 + [(5-2x)(5-2x)] =10
x^2 + [25 -10x -10x + 4x^2] =10
5x^2 -20x + 15

Divide through by 5

x^2 -4x + 3 = 0

Now complete the square (there is an equation you can use if you can't see it automatically)

However

(x-1)(x-3) = x^2 -4x +3 = 0 Therefore x=1 or 3 as these make the equation zero.

Plug back in to the equation to give y,

so y = 3 or -1

As you will see their are four answers to the question. My apologies for confusing you earlier.
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Postby pinkparrot » Mon Oct 31, 2005 9:33 pm

I can see we understand each other. What about Miranda?
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Postby Miranda » Tue Nov 01, 2005 12:09 am

nope sorry
i havent a clue :oops: :(
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Postby pinkparrot » Tue Nov 01, 2005 8:05 am

I know this is hard, because I get in knots with it myself, but can you try to tell me what it is about this algebra question that you don't understand?
Don't worry if you don't know.
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Postby Pookie » Tue Nov 01, 2005 9:46 am

As pinkparrot says, have a look at my example and tell us exactly at which point you don't follow.
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Postby monkey » Tue Nov 01, 2005 10:36 am

i enjoy algebra but im terrible at it :)
but there seems to be a cuple of people who are very good at it. good luck
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Postby Miranda » Tue Nov 01, 2005 5:33 pm

how do u know what to substitute when?
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Postby Pookie » Tue Nov 01, 2005 5:51 pm

You have two unknowns x and y, both equations contain x and y.

You need to make one equation contain 'only x' to make it possible to solve.

re-arrange the easiest equation which in this case is 2x+y=5 so it is y=5-2x.

Now because we know y=5-2x then it follows y^2=(5-2x)^2 so we can substitute (5-2x)^2 in place of y^2 in your first equation then tidy it all up to make it possible to solve.

If you missed the algebraic course then my reccomendation is to approach your teacher for some extra study lessons or perhaps then can provide you with some teaching material and extra questions for you to practise on and catch up.
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Postby parnassus » Tue Nov 01, 2005 8:22 pm

I can't help you with algebra, Miranda (dyscalculia frustrates the best of intentions!) but I could try and put you in touch with an Oxford maths student. He tutored me during my GCSE course and he was v. kind. I'll contact him for you. If he's too busy with his work, I'm sure I could find a Cambridge 'mathmo' who would be delighted to help - like that very enthusiastic economics student who was lecturing me on Middle Eastern inflation last night.

On second thoughts, I would feel very guilty if you got lumbered with that!

As regards the rest of your schoolwork, remember my offer of the study timetable. I will send you a copy of my own to show you how I keep motivated.
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Postby pinkparrot » Tue Nov 01, 2005 8:51 pm

Algebra is one of those things where you have to turn back to the basics every 10 minutes or you risk losing your head, which I have done. Always ensure you know what you are doing. I prefer learning the correct method first rather than learning several wrong ones, then the correct one.
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Postby Miranda » Tue Nov 01, 2005 9:00 pm

It sounds interesting
i have walked 8 miles listening to the taiwanese infrastructure, i quite enjoy that stuff, and yeah that would be great, my maths teacher just wants me to drop a few sets and take intermediate tier, im useless at maths but i want to do alright in it nonetheless
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Postby parnassus » Tue Nov 01, 2005 9:26 pm

I took intermediate tier and achieved a C. It is possible to get a B on that tier, so I think it might be sensible if you moved down. After all, you can't be an A* candidate in everything, and if you are really struggling you are more likely to do well on the intermediate paper than the higher.

I'll send you the timetable tomorrow, once I've typed it up neatly. I have also written to my mathmo friend to see what he says.

By the way, what is Taiwanese infrastructure? I take it it's a band and not a construction company.
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Postby Pookie » Tue Nov 01, 2005 10:24 pm

parnassus wrote:By the way, what is Taiwanese infrastructure? I take it it's a band and not a construction company.


This amused me :lol:
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