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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

HI,

I am very weak in match, i have equation like

1. 3x-2y=1 h

2. 3x+y = x+3

Please help

Lokesh

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi;

What is that h doing there?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

i m doing set theory

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

I do not understand, aren't you solving a simultaneous set of linear equations? What has that to do with set theory? Is that h a variable?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

quiz is this . find x and y if (3x+y, x-1) = (x+3, 2y-2x)

sorry h is mistake , h is nothing

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

this question is from ordered pairs, so that first i have to find x and y

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

I am getting x = 1 and y = 1.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

yes, perfect, is there any method or something else to find value of x and y?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

There are several methods:

Form the simultaneous set:

Do you know how to solve that?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

no, i don't know

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Clean this one up a bit by subtracting x from both sides.

Clean up the second one

Add 2x to both sides

Subtract 2y from both sides.

Add one to both sides

We now have

Did you follow up to here?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

how do you think what to add or not?

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

ya i got it till here, but what next to find x and y?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

how do you think what to add or not?

Just trying to get it into the form of all the variables on the left and all the numbers on the right so we can make the next bunch of moves.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

ok, but what will be the next step to find x value?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

We would like to subtract or add the bottom equation from the top one and make one variable disappear. But when I do that 2x - 3x = x, that did not disappear and y + (-2y) = y so no luck there either.

If I multiply the top equation by 3 I get

Now if I multiply the second equation by 2 I get

So I have changed the equations again to

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**lokitwister****Member**- Registered: 2013-01-31
- Posts: 10

Thanks, here i will find y

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Can you finish now or do you want me to do more?

Where did he go?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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