document.write( "Question 258000: What is the points of intersection of these equations
\n" ); document.write( "x-2y-8=0
\n" ); document.write( "x^2=y^2-12x+6y+29=0 \n" ); document.write( "
Algebra.Com's Answer #189916 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Note: The other two tutors' solutions are both incorrect.\r\n" );
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document.write( "\"system%28x-2y-8=0%2C+x%5E2%2By%5E2-12x%2B6y%2B29=0%29\"\r\n" );
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document.write( "Solve the first equation for x\r\n" );
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document.write( "\"x-2y-8=0\"\r\n" );
document.write( "\"x=2y%2B8\"\r\n" );
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document.write( "Substitute \"%282y%2B8%29\" for x in the second equation:\r\n" );
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document.write( "\"x%5E2%2By%5E2-12x%2B6y%2B29=0\"\r\n" );
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document.write( "\"%282y%2B8%29%5E2%2By%5E2-12%282y%2B8%29%2B6y%2B29=0\"\r\n" );
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document.write( "\"%282y%2B8%29%282y%2B8%29%2By%5E2-12%282y%2B8%29%2B6y%2B29=0\"\r\n" );
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document.write( "\"%284y%5E2%2B16y%2B16y%2B64%29%2By%5E2-12%282y%2B8%29%2B6y%2B29=0\"\r\n" );
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document.write( "\"4y%5E2%2B32y%2B64%2By%5E2-24y-96%2B6y%2B29=0\"\r\n" );
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document.write( "\"5y%5E2%2B14y-3=0\"\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "\"%285y-1%29%28y%2B3%29=0\"\r\n" );
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document.write( "Use zero-factor principle:\r\n" );
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document.write( "\"5y-1=0\" gives solution \"y=1%2F5\"\r\n" );
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document.write( "\"y%2B3=0\" gives solution \"y=-3\"\r\n" );
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document.write( "Now we must find the value of x for each of these\r\n" );
document.write( "two values for y.\r\n" );
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document.write( "For \"y=1%2F5\" we substitute \"%281%2F5%29\" for y in \r\n" );
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document.write( "\"x=2y%2B8\"\r\n" );
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document.write( "\"x=2%281%2F5%29%2B8\"\r\n" );
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document.write( "\"x=2%2F5%2B8\"\r\n" );
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document.write( "\"x=2%2F5%2B40%2F5\"\r\n" );
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document.write( "\"x=42%2F5%29+%0D%0A%0D%0ASo+one+solution+is+%28x%2Cy%29+=+%28%7B%7B%7B42%2F5\",\"1%2F5\")\r\n" );
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document.write( "or if you prefer, (x,y) = (8.4,.2)\r\n" );
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document.write( "For \"y=-3\" we substitute \"%28-3%29\" for y in \r\n" );
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document.write( "\"x=2y%2B8\"\r\n" );
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document.write( "\"x=2%28-3%29%2B8\"\r\n" );
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document.write( "\"x=-6%2B8\"\r\n" );
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document.write( "\"x=2\"\r\n" );
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document.write( "So the other solution is (x,y) = (2,-3)\r\n" );
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document.write( "Edwin
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