document.write( "Question 1186043: Solve this simultaneous equation:
\n" ); document.write( "\"%283%2Fx%29+-+%284%2Fy%29+=+%281%2F3%29\", \"%282%2Fx%29+-+%285%2Fy%29+=%281%29\"
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Algebra.Com's Answer #816907 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"%283%2Fx%29+-+%284%2Fy%29+=+%281%2F3%29\", \"%282%2Fx%29+-+%285%2Fy%29+=%281%29\"
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document.write( "    \"%283%2Fx%29+-+%284%2Fy%29\" = \"1%2F3\"    (1)\r\n" );
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document.write( "    \"%282%2Fx%29+-+%285%2Fy%29\" = 1.    (2)\r\n" );
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document.write( "Introduce new variables  u = \"1%2Fx\",  v = \"1%2Fy\".  with these variables, the equations take the form\r\n" );
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document.write( "    3u - 4v = \"1%2F3\"      (3)\r\n" );
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document.write( "    2u - 5v = 1.      (4)\r\n" );
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document.write( "To solve it use the Elimination method.\r\n" );
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document.write( "    6u -  8v = \"2%2F3\"    (5)\r\n" );
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document.write( "    6u - 15v = 3      (6)\r\n" );
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document.write( "  ------------------------------- Subtract eq(5) from eq(6)\r\n" );
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document.write( "        -7v = 2 \"1%2F3\" = \"7%2F3\"\r\n" );
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document.write( "          v = \"-1%2F3\".\r\n" );
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document.write( "Substitute v = -1/3  into equation (6) to get  \r\n" );
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document.write( "    6u = 3 - 5 = -2,\r\n" );
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document.write( "     u         = \"-2%2F6\" = \"-1%2F3\".\r\n" );
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document.write( "ANSWER.  x = \"1%2Fu\" = \"1%2F%28%28-1%2F3%29%29\" = -3.   y = \"1%2Fv\" = \"1%2F%28%28-1%2F3%29%29\" = -3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Introducing new variables is one of standard methods solving such equations.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems,  look into the lesson\r
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