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VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: #1procrastinator on August 10, 2011, 05:06:37 pm

Title: Simultaneous equations
Post by: #1procrastinator on August 10, 2011, 05:06:37 pm

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

Title: Re: Simultaneous equations
Post by: pi on August 10, 2011, 05:08:51 pm

Quote from: #1procrastinator on August 10, 2011, 05:06:37 pm

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.

Title: Re: Simultaneous equations
Post by: Tomanomanous on August 20, 2011, 06:57:17 pm

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

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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]

Title: Re: Simultaneous equations
Post by: acinod on August 20, 2011, 08:18:20 pm

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.