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 September 4th, 2015, 04:35 AM #1 Senior Member   Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4 Transformation question Hello, If v=x-2y and u=2x-y, to what line will x=y transform in the u,v plane? I don't understand how am I supposed to find the line in terms of u,v plane . Thanks! September 4th, 2015, 06:11 AM   #2
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 Originally Posted by noobinmath Hello, If v=x-2y and u=2x-y, to what line will x=y transform in the u,v plane? I don't understand how am I supposed to find the line in terms of u,v plane . Thanks!
It simply means x=y in form of u and v
1st take out the value of x and y
X=(2u-v)/3
Y=(u-2v)/3        Now x=y September 4th, 2015, 06:12 AM   #3
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 Originally Posted by Yash Malik It simply means x=y in form of u and v 1st take out the value of x and y X=(2u-v)/3 Y=(u-2v)/3        Now x=y
U=-v or
u+v=0  September 4th, 2015, 06:36 AM #4 Senior Member   Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4 Thanks!    This is really the anwer! But how did you find out so easily that x=(2u-v)/3 for example? September 4th, 2015, 06:50 AM #5 Senior Member   Joined: Sep 2015 From: 4th Dimension Posts: 146 Thanks: 13 Math Focus: Everything (a little bit) Practice makes a man perfect Thanks from noobinmath September 4th, 2015, 07:07 AM   #6
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Quote:
 Originally Posted by noobinmath v=x-2y and u=2x-y
There are many ways to solve this for x and y. Probably the simplest way is to proceed like this:
$\displaystyle \left \{ \begin{matrix} v = x - 2y \\ u = 2x - y \end{matrix} \right .$

Multiply the top equation by 2 and the bottom equation by -1
$\displaystyle \left \{ \begin{matrix} 2v = 2x - 4y \\ -u = -2x + y \end{matrix} \right .$

Now add the two equations:
$\displaystyle (2v - u) = (2x - 2x) + (-4 + 1)y$

$\displaystyle 2y - u = -3y$

$\displaystyle y = \frac{1}{3} (u - 2v)$

You can do a similar thing with the original equations to get the expression for x, or you could put $\displaystyle y = \frac{1}{3} (u - 2v)$ into either of the original equations and solve for x.

-Dan September 4th, 2015, 07:08 AM #7 Senior Member   Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4 Haha I will try again I was just playing with these two equations for quite some time and didn't get to separate x and y! always ended up with x=y or 0=0 etc!!     edit: Thanks Dan! September 4th, 2015, 07:22 AM #8 Senior Member   Joined: Sep 2015 From: 4th Dimension Posts: 146 Thanks: 13 Math Focus: Everything (a little bit) Gd job Dan i am a bit lazy so i didn't show the complete steps Btw plz solve my limits question Thanks from noobinmath Tags question, transformation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post zion3012 Algebra 3 November 17th, 2012 04:37 AM MikaelUmaN Advanced Statistics 0 October 20th, 2012 07:58 AM lechatelier Algebra 10 April 30th, 2012 01:49 AM sheena107 Algebra 1 September 21st, 2009 05:20 AM brakson Algebra 0 February 12th, 2008 10:19 AM

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