document.write( "Question 305894: Im REALLY stuck on this Algebra Equasion, Please Help Me!!!
\n" ); document.write( "I have these two formulas
\n" ); document.write( "12-x^2 -2xy = 0
\n" ); document.write( "12-y^2 - 2xy = 0
\n" ); document.write( "for some reason x and y are both 2
\n" ); document.write( "how do you get this
\n" ); document.write( "i tried and got
\n" ); document.write( "y= 6/x -0.5x tried to sub into second one but gets messy any way to do this on a calculator by any chance i have a Ti-83 but i want to know how to do it algebraically hmmmmm........ \n" ); document.write( "

Algebra.Com's Answer #218977 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. $\"12-x%5E2+-2xy+=+0\"$
\n" ); document.write( "2. $\"12-y%5E2+-+2xy+=+0\"$
\n" ); document.write( "Use eq. 1 to solve for y.
\n" ); document.write( "1. $\"12-x%5E2+-2xy+=+0\"$
\n" ); document.write( " $\"12-x%5E2=2xy\"$
\n" ); document.write( " $\"y=%2812-x%5E2%29%2F2x\"$
\n" ); document.write( "From that, then,
\n" ); document.write( " $\"y%5E2=+%2812-x%5E2%29%5E2%2F%284x%5E2%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"2xy=12-x%5E2\"$
\n" ); document.write( "Substitute into eq. 2,
\n" ); document.write( "2. $\"12-y%5E2+-+2xy+=+0\"$
\n" ); document.write( " $\"12-+%2812-x%5E2%29%5E2%2F%284x%5E2%29+-+%2812-x%5E2%29+=+0\"$
\n" ); document.write( " $\"-+%2812-x%5E2%29%5E2%2F%284x%5E2%29+%2Bx%5E2+=+0\"$
\n" ); document.write( " $\"+%2812-x%5E2%29%5E2%2F%284x%5E2%29+=x%5E2\"$
\n" ); document.write( " $\"+%2812-x%5E2%29%5E2+=4x%5E4\"$
\n" ); document.write( " $\"+12-x%5E2+=0+%2B-+2x%5E2\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"12-x%5E2=2x%5E2\"$
\n" ); document.write( " $\"3x%5E2=12\"$
\n" ); document.write( " $\"x%5E2=4\"$
\n" ); document.write( " $\"x=2\"$ and $\"x=-2\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"12-x%5E2=-2x%5E2\"$
\n" ); document.write( " $\"-x%5E2=12\"$
\n" ); document.write( " $\"x%5E2=-12\"$
\n" ); document.write( "No real solution.
\n" ); document.write( ".
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\n" ); document.write( "When $\"x=-2\"$ ,
\n" ); document.write( " $\"y=%2812-x%5E2%29%2F2x\"$
\n" ); document.write( " $\"y=%2812-4%29%2F2%28-2%29\"$
\n" ); document.write( " $\"y=-2\"$
\n" ); document.write( "When $\"x=2\"$ ,
\n" ); document.write( " $\"y=%2812-x%5E2%29%2F2x\"$
\n" ); document.write( " $\"y=%2812-4%29%2F4\"$
\n" ); document.write( " $\"y=2\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "(-2,-2) and (2,2) are the solutions.
\n" ); document.write( ".
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\n" ); document.write( "You are searching for the intersection point between two curves.
\n" ); document.write( "The first curve is
\n" ); document.write( " $\"y=%2812-x%5E2%29%2F2x\"$ (in red below)
\n" ); document.write( "The second curve needs to be worked out by completing the square for the second equation,
\n" ); document.write( " $\"12-y%5E2+-+2xy+=+0\"$
\n" ); document.write( " $\"12=y%5E2%2B2xy\"$
\n" ); document.write( " $\"12%2Bx%5E2=y%5E2%2B2xy%2Bx%5E2\"$
\n" ); document.write( " $\"12%2Bx%5E2=%28y%2Bx%29%5E2\"$
\n" ); document.write( " $\"0+%2B-+sqrt%2812%2Bx%5E2%29=y%2Bx\"$
\n" ); document.write( " $\"y=-x+%2B-+sqrt%2812%2Bx%5E2%29\"$ (in blue and green below)
\n" ); document.write( "The curves and the two solution points are shown below.
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