September 4th, 2015, 04:35 AM  #1 
Senior Member Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4  Transformation question
Hello, If v=x2y and u=2xy, 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  
Senior Member Joined: Sep 2015 From: 4th Dimension Posts: 146 Thanks: 13 Math Focus: Everything (a little bit)  Quote:
1st take out the value of x and y X=(2uv)/3 Y=(u2v)/3 Now x=y  
September 4th, 2015, 06:12 AM  #3 
Senior Member Joined: Sep 2015 From: 4th Dimension Posts: 146 Thanks: 13 Math Focus: Everything (a little bit)  
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=(2uv)/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 
September 4th, 2015, 07:07 AM  #6 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,256 Thanks: 926 Math Focus: Wibbly wobbly timeywimey stuff.  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 

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