My Math Forum Transformation question

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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
$\displaystyle \left \{ \begin{matrix} 2v = 2x - 4y \\ -u = -2x + y \end{matrix} \right .$

$\displaystyle (2v - u) = (2x - 2x) + (-4 + 1)y$

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

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

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

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