Algebra.Com's Answer #657839 by ikleyn(52788)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "I Need help with solving an equation in two variables using elimination method. Here's the sum: 11x - 7y =xy , 9x - 4y = 6xy please.?
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document.write( "11x - 7y = xy, (1)\r\n" );
document.write( " 9x - 4y = 6xy. (2)\r\n" );
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document.write( "There is more elegant solution. Let me show it.\r\n" );
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document.write( "Divide both sides of (1) by xy. Divide both sides of (2) by xy. You will get\r\n" );
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document.write( " = 1, (1')\r\n" );
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document.write( " = 6. (2')\r\n" );
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document.write( "Now introduce new variables u =  , v =  . Then (1') and (2') take the form\r\n" );
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document.write( "11u - 7v = 1, (1'')\r\n" );
document.write( " 9u - 4v = 6. (2'')\r\n" );
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document.write( "It is usual system of two linear equations in two unknowns.\r\n" );
document.write( "You can easily solve it using the Elimination method in its standard form. It is just simple technique, let me do not continue.\r\n" );
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document.write( "When you find u and v, do not forget to return back to the original x and y.\r\n" );
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document.write( "In order to make this approach absolutely clean, you must justify dividing by xy of equations (1) and (2). \r\n" );
document.write( "It means that you must accurately analyse the case xy = 0. \r\n" );
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document.write( "If xy = 0, then x=0 or y=0 (or both).\r\n" );
document.write( "If x=0, then from equations (1),(2) y=0.\r\n" );
document.write( "If y=0, then from equations (1),(2) x=0.\r\n" );
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document.write( "Thus x=0, y=0 is one solution of (1), (2).\r\n" );
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document.write( "The other solution comes from the procedure described above.\r\n" );
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document.write( "For close melody problems see the lesson\r
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document.write( " - Solving systems of non-linear equations in two unknowns using the Cramer's rule \r
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document.write( "in this site.\r
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