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April 20, 2024, 03:13:02 am
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Author Topic: Simultaneous linear equations.  (Read 1076 times)  Share 

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JR_StudyEd

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Simultaneous linear equations.
« on: August 08, 2019, 09:58:56 pm »
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You know those questions that go:

The simultaneous linear equations ____ and _____ have no/a unique/infinitely many solution(s) provided...? I don't know how to do them, and I don't understand what the ATAR Notes book says about it...  :-[
Hopefully I clearly articulated my problem to you...Please help me out. Thanks.
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^^^111^^^

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Re: Simultaneous linear equations.
« Reply #1 on: August 08, 2019, 10:04:58 pm »
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Quote from: JR_StudyEd on August 08, 2019, 09:58:56 pm
You know those questions that go:

The simultaneous linear equations ____ and _____ have no/a unique/infinitely many solution(s) provided...? I don't know how to do them, and I don't understand what the ATAR Notes book says about it...  :-[
Hopefully I clearly articulated my problem to you...Please help me out. Thanks.
Edit:Hey JR, nice to meet you! If  simulatenous linear equations were the same that means they have infinite solutions. If they are perpendicular to each other, they have 1 solutions, else unique solutions. And if they are parallel then there are no solutions. E.g.
y=2x+5 and y=2x+3 have no solutions since they are parallel (same gradient). y=2x+5 and y=-1/2x+ 3 have one solution.
« Last Edit: August 09, 2019, 07:42:27 am by ^^^111^^^ »
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SmellsLikeTeenSpirit

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Re: Simultaneous linear equations.
« Reply #2 on: August 08, 2019, 11:10:38 pm »
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Hi JR,

I have attached two gif files - the first one shows graphically the difference between those different cases (unique solution; no solution, infinitely many solutions), the second one provides numerical examples.

Hope this helps
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^^^111^^^

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Re: Simultaneous linear equations.
« Reply #3 on: August 09, 2019, 07:43:31 am »
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Quote from: SmellsLikeTeenSpirit on August 08, 2019, 11:10:38 pm
Hi JR,

I have attached two gif files - the first one shows graphically the difference between those different cases (unique solution; no solution, infinitely many solutions), the second one provides numerical examples.

Hope this helps
I just realised my mistake. Thank you!
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kimokeeffe

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Re: Simultaneous linear equations.
« Reply #4 on: August 19, 2019, 05:46:05 pm »
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Hello! the way i like to work these out is by first working out the gradient of the lines, if they have the same gradient then you know they are either parallel (no solutions) or the same line (infinite solutions). Then you can work out if they have the same 'c' (y=mx+c), if they do then they are the same line and have infinite solutions, if not they are parallel so have no solutions! hope this helps :)
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