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March 29, 2024, 05:24:50 am

Author Topic: Simultaneous equations  (Read 1313 times)  Share 

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#1procrastinator

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Simultaneous equations
« on: August 10, 2011, 05:06:37 pm »
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2x + y = 10
y = 10 - 2x

Why does it make no mathematical sense to replace y with (10 - 2x) in that equation besides the fact that you have no variables left

pi

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Re: Simultaneous equations
« Reply #1 on: August 10, 2011, 05:08:51 pm »
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2x + y = 10
y = 10 - 2x

Why does it make no mathematical sense to replace y with (10 - 2x) in that equation besides the fact that you have no variables left

Because both lines are the same... Hence, there are infinite solutions? A substitution will just get 0=0.

Your method works fine as long as the linear equations are not the same/parallel.

Tomanomanous

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Re: Simultaneous equations
« Reply #2 on: August 20, 2011, 06:57:17 pm »
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2x+y= 10
y=10-2x

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2x+(10-2x)=10
Substitute the y value in as you know what it equals

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2x+10-2x=10

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0=0

------------------------------------------------

AND

2x+y=10
y=10-2x <- From moving the 2x to the other side.

So really you're working with the same rule.[/align]
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acinod

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Re: Simultaneous equations
« Reply #3 on: August 20, 2011, 08:18:20 pm »
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The formal solution is:

2x+y=10...(1)
y=10-2x...(2)
From (1): y=10-2x...(3)
(3) is the same as (2)
Let y=k where k is a real number
Sub y=k into (2): k=10-2x -> x=(10-k)/2

Solutions: x=(10-k)/2 and y=k where k is any real number.
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