document.write( "Question 353523: Find numerical values for all simultaneous solutions of:
\n" ); document.write( "X^2+3y^2=27
\n" ); document.write( "xy=6\r
\n" ); document.write( "\n" ); document.write( "and illustrate with a graph \n" ); document.write( "

Algebra.Com's Answer #252591 by robertb(5830) $\"\"$ $\"About$

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$\"x%5E2+%2B+3%2Ax%5E2=27\"$ (1)
\n" ); document.write( " $\"xy+=+6\"$ (2)
\n" ); document.write( "From equation (2), $\"y+=+6%2Fx\"$ .
\n" ); document.write( "Substituting into (1),
\n" ); document.write( " $\"x%5E2+%2B3%2A%286%2Fx%29%5E2=27\"$ ,
\n" ); document.write( " $\"x%5E2+%2B+108%2Fx%5E2=27\"$ ,
\n" ); document.write( "Multiplying both sides by $\"x%5E2\"$ , we get
\n" ); document.write( " $\"x%5E4+%2B108+=+27%2Ax%5E2\"$ , or
\n" ); document.write( " $\"x%5E4+-+27%2Ax%5E2+%2B+108+=+0\"$ . Treating the equation as a quadratic equation in $\"x%5E2\"$ , and applying the quadratic formula, we get
\n" ); document.write( " $\"x%5E2+=+%2827+%2B-+sqrt%2827%5E2-4%2A1%2A108%29%29%2F2\"$ ,
\n" ); document.write( " $\"x%5E2+=+%2827%2B-sqrt%28297%29%29%2F2\"$ . Hence
\n" ); document.write( " $\"x+=+sqrt%28%2827%2B-sqrt%28297%29%29%2F2%29\"$ , or
\n" ); document.write( " $\"x+=+-sqrt%28%2827%2B-sqrt%28297%29%29%2F2%29\"$ . The values that we get from the first x-value are $\"x+=+4.703\"$ or $\"2.2098\"$ . from the second x-value, we get the negatives: $\"x+=+-4.703\"$ or $\"-2.2098\"$ .
\n" ); document.write( "The corresponding y-values are (obtained from equation (2)) 1.2758, 2.7152,
\n" ); document.write( "-1.2758, -2.7152.\r
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