document.write( "Question 681944: How would you solve the substitution equation:
\n" ); document.write( "x+y=1
\n" ); document.write( "X^2+xy-y^2=-1\r
\n" ); document.write( "\n" ); document.write( "Thank you. \n" ); document.write( "

Algebra.Com's Answer #422970 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%2By=1\"$ ...............1\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bxy-y%5E2=-1\"$ ........2
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\n" ); document.write( "\n" ); document.write( " $\"x%2By=1\"$ ...............1...solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=1-y\"$ .......substitute in 2
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bxy-y%5E2=-1\"$ ........2\r
\n" ); document.write( "\n" ); document.write( " $\"%281-y%29%5E2%2B%281-y%29y-y%5E2=-1\"$ .........solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1-2y%2By%5E2%2By-y%5E2-y%5E2=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1-2y%2Bcross%28y%5E2%29%2By-cross%28y%5E2%29-y%5E2=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1-y-y%5E2=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1%2B1-y-y%5E2=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y%5E2%2By-2=0\"$ ...use quadratic formula\r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-2%29+%29%29%2F%282%2A1%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28-1+%2B-+sqrt%28+1%2B8+%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28-1+%2B-+sqrt%289%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28-1+%2B-+3%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28-1+%2B3%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+2%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+1+\"$ \r
\n" ); document.write( "\n" ); document.write( "and \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28-1+-3%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+-4%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+-2+\"$ \r
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\n" ); document.write( "\n" ); document.write( "now find $\"x\"$ \r
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\n" ); document.write( "\n" ); document.write( "if $\"y+=+1+\"$ :\r
\n" ); document.write( "\n" ); document.write( " $\"x=1-y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=1-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "if $\"y+=+-2+\"$ :\r
\n" ); document.write( "\n" ); document.write( " $\"x=1-%28-2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=1%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( "so, solution pairs are:\r
\n" ); document.write( "\n" ); document.write( "1. $\"y+=+1+\"$ and $\"x=0\"$ \r
\n" ); document.write( "\n" ); document.write( "2. $\"y+=+-2+\"$ and $\"x=3\"$ \r
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