document.write( "Question 468875: plaase help me solve this system equations x+2y+2xy=3 and 3x+4y-2xy=4 \n" ); document.write( "
Algebra.Com's Answer #321719 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " x + 2y + 2xy = 3\r\n" );
document.write( "3x + 4y - 2xy = 4\r\n" );
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document.write( "Solve the first one for x\r\n" );
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document.write( " x + 2y + 2xy = 3\r\n" );
document.write( "      x + 2xy = 3 - 2y\r\n" );
document.write( "    x(1 + 2y) = 3 - 2y\r\n" );
document.write( "            x = \"%283-2y%29%2F%281%2B2y%29\"\r\n" );
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document.write( "3x + 4y - 2xy = 4\r\n" );
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document.write( "3(\"%283-2y%29%2F%281%2B2y%29\") + 4y - 2(\"%283-2y%29%2F%281%2B2y%29\")y = 4\r\n" );
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document.write( "Multiply through by \"%281%2B2y%29\"\r\n" );
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document.write( "3(3 - 2y) + 4y(1 + 2y) - 2(3 - 2y)y = 4(1 + 2y)\r\n" );
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document.write( "3(3 - 2y) + 4y(1 + 2y) - 2y(3 - 2y) = 4(1 + 2y)\r\n" );
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document.write( "       9 - 6y + 4y + 8y² - 6y + 4y² = 4 + 8y\r\n" );
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document.write( "                      9 - 8y + 12y² = 4 + 8y\r\n" );
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document.write( "Get 0 on the right side:\r\n" );
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document.write( "                     12y² - 16y + 5 = 0  \r\n" );
document.write( "Factor:\r\n" );
document.write( "                   (2y - 1)(6y - 5) = 0\r\n" );
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document.write( "Use zero-factor property:\r\n" );
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document.write( "          2y - 1 = 0         6y - 5 = 0\r\n" );
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document.write( "              2y = 1             6y = 5\r\n" );
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document.write( "               y = \"1%2F2\"             y = \"5%2F6\"\r\n" );
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document.write( "So there are going to be two solutions.  We must find\r\n" );
document.write( "the x-value that corresponds to each one.\r\n" );
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document.write( "Find the x-value that corresponds to y = \"1%2F2\"\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "x = \"%283-2y%29%2F%281%2B2y%29\"\r\n" );
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document.write( "x = \"%283-2%281%2F2%29%29%2F%281%2B2%281%2F2%29%29\"\r\n" );
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document.write( "x = \"%283-1%29%2F%281%2B1%29\" = \"2%2F2\" = 1\r\n" );
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document.write( "So one solution is (x,y) = (1,\"1%2F2\")\r\n" );
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document.write( "Find the x-value that corresponds to y = \"5%2F6\"\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "x = \"%283-2y%29%2F%281%2B2y%29\"\r\n" );
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document.write( "x = \"%283-2%285%2F6%29%29%2F%281%2B2%285%2F6%29%29\"\r\n" );
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document.write( "x = \"%283-10%2F6%29%2F%281%2B10%2F6%29\" = \"%283-5%2F3%29%2F%281%2B5%2F3%29\" \r\n" );
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document.write( "Multiply top and bottom by 3\r\n" );
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document.write( "x = \"%283%283-5%2F3%29%29%2F%283%281%2B5%2F3%29%29\" = \"%289-5%29%2F%283%2B5%29\" = \"4%2F8\" = \"1%2F2\"\r\n" );
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document.write( "So the other solution solution is (x,y) = (\"1%2F2\",\"5%2F6\")\r\n" );
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document.write( "Edwin
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