document.write( "Question 30022: Find the real Solutions, if any, of each system.\r
\n" ); document.write( "\n" ); document.write( "\"xy+=+2\"
\n" ); document.write( "\"x%5E2+%2B+y%5E2+=+4\"\r
\n" ); document.write( "\n" ); document.write( "The answers for this are
\n" ); document.write( "(Square Root of 2, Square root of 2)
\n" ); document.write( "(-Square Root of 2, -Square root of 2)
\n" ); document.write( "Thankyou,I have the answers, I just need to know how to go about doing these types of problems.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #16766 by sdmmadam@yahoo.com(530)\"\" \"About 
You can put this solution on YOUR website!
xy = 2 ----(1)
\n" ); document.write( "x^2 + y^2 = 4 ----(2)
\n" ); document.write( "Use the standard formula
\n" ); document.write( "(x-y)^2 = x^2+y^2 - 2xy
\n" ); document.write( "=4 -2X(2) using (2) and (1)
\n" ); document.write( "=4-4 = 0
\n" ); document.write( "(x-y) ^2 = 0
\n" ); document.write( "Therefore taking sqrt
\n" ); document.write( "(x-y) = 0 ----(3)
\n" ); document.write( "Which means x = y ----(3)
\n" ); document.write( "Putting x=y in (1)
\n" ); document.write( "xy = 2
\n" ); document.write( "yXy = 2
\n" ); document.write( "y^2 = 2
\n" ); document.write( "y = +or - root(2)
\n" ); document.write( "y = +[root(2)] implies from (3) x also = +[root(2)]
\n" ); document.write( "y = -[root(2)] implies from (3) x also = -[root(2)]
\n" ); document.write( "Answer: x = sqrt2, y = sqrt2 (one set of answers)
\n" ); document.write( "x = -sqrt2, y = -sqrt2 (another set of answers)
\n" ); document.write( "And both sets hold (on oral verification itself)\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );