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April 30th, 2015, 10:00 AM  #1 
Member Joined: Feb 2014 Posts: 91 Thanks: 1  Where did this exponent come from? Not sure about this, please assist. 
April 30th, 2015, 10:37 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,847 Thanks: 1486 
you were given ... $y^2=5x^2$ $y = x1$ substitute $(x1)$ for $y$ in the first equation ... $(x1)^2 = 5x^2$ 
April 30th, 2015, 10:39 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
You are given the two equations $\displaystyle x^2+ y^2= 5$ and $\displaystyle x y= 1$. Subtrating $\displaystyle x^2$ from both sides of the first equation, $\displaystyle y^2= 5 x^2$ Adding y to both sides of the second equation, $\displaystyle x= 1+ y$. Subtracting 1 from both sides of that equation, $\displaystyle x 1= y$ So we can replace y by x 1 in $\displaystyle y^2= 5 x^2$: $\displaystyle (x 1)^2= 5 x^2$. Essentially then the exponent, 2, in that equation come form the exponent on y in the equation $\displaystyle x^2+ y^2= 5$. 
May 1st, 2015, 07:21 PM  #4 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry 
If you are that confused, just write y = y between the second and the third line, hope you understand.


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