document.write( "Question 1021116: Solve each system of equations:
\n" ); document.write( "{3x^2+4xy+5y^2=8 and x^2+3xy+2y^2=0
\n" ); document.write( "When I try to solve it, it turns out to be really messy. PLease use elimination or substituion in your answer. Thank you \n" ); document.write( "

Algebra.Com's Answer #636922 by robertb(5830) $\"\"$ $\"About$

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$\"3x%5E2%2B4xy%2B5y%5E2=8+\"$ (Equation A)\r
\n" ); document.write( "\n" ); document.write( " $\"+x%5E2%2B3xy%2B2y%5E2=0\"$ (Equation B)\r
\n" ); document.write( "\n" ); document.write( "The key lies in factoring Eqn. B: $\"+x%5E2%2B3xy%2B2y%5E2=0\"$ <==> (x+y)(x+2y) = 0.
\n" ); document.write( "We discuss 2 cases:
\n" ); document.write( "(i) When x+y = 0, or y = -x. Substitute this into Eqn.A
\n" ); document.write( "==> $\"3x%5E2-4x%5E2%2B5x%5E2+=+8\"$ ==> $\"4x%5E2+=+8\"$ ==> $\"x%5E2+=+2\"$
\n" ); document.write( "==> $\"x+=sqrt%282%29\"$ or $\"x+=+-+sqrt%282%29\"$
\n" ); document.write( "==> the solutions ( $\"sqrt%282%29\"$ , $\"-sqrt%282%29\"$ ) and ( $\"-sqrt%282%29\"$ , $\"sqrt%282%29\"$ ).\r
\n" ); document.write( "\n" ); document.write( "(ii) The case of x+2y = 0, or x = -2y, is handled in a similar manner.
\n" ); document.write( "After doing so we get the pair of solutions ( $\"-4sqrt%282%29%2F3\"$ , $\"2sqrt%282%29%2F3\"$ ) and ( $\"4sqrt%282%29%2F3\"$ , $\"-2sqrt%282%29%2F3\"$ ).\r
\n" ); document.write( "\n" ); document.write( "Therefore the solutions are ( $\"sqrt%282%29\"$ , $\"-sqrt%282%29\"$ ), ( $\"-sqrt%282%29\"$ , $\"sqrt%282%29\"$ ), ( $\"-4sqrt%282%29%2F3\"$ , $\"2sqrt%282%29%2F3\"$ ), and ( $\"4sqrt%282%29%2F3\"$ , $\"-2sqrt%282%29%2F3\"$ ).\r
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