document.write( "Question 79234: Solve each system by the addition method.\r
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Algebra.Com's Answer #56878 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Solve each system by the addition method.\r\n" );
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document.write( "x/3 - y/2 = -5/6\r\n" );
document.write( "x/5 - y/3 = -3/5\r\n" );
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document.write( "\"%28x%2F3%29+-+%28y%2F2%29+=+-5%2F6\"\r\n" );
document.write( "\"%28x%2F5%29+-+%28y%2F3%29+=+-3%2F5\"\r\n" );
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document.write( "You should clear of fractions first.\r\n" );
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document.write( "Clear the first of fractions by multiplying \r\n" );
document.write( "through by \"6%2F1\": \r\n" );
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document.write( "\"%286%2F1%29%28x%2F3%29+-+%286%2F1%29%28y%2F2%29+=+%286%2F1%29%28-5%2F6%29\"\r\n" );
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document.write( "   2x - 3y = -5\r\n" );
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document.write( "Clear the second of fractions by multiplying \r\n" );
document.write( "through by \"15%2F1\": \r\n" );
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document.write( "x/5 - y/3 = -3/5\r\n" );
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document.write( "\"%2815%2F1%29%28x%2F5%29+-+%2815%2F1%29%28y%2F3%29+=+%2815%2F1%29%28-3%2F5%29\"\r\n" );
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document.write( "   3x - 5y = -9\r\n" );
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document.write( "So we have the system\r\n" );
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document.write( "   2x - 3y = -5\r\n" );
document.write( "   3x - 5y = -9\r\n" );
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document.write( "The coefficients of y are -3 and -5. The LCM of\r\n" );
document.write( "their absolute values is 15, so \r\n" );
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document.write( "1. We need to make the -3 in the first into a -15 \r\n" );
document.write( "by multiplyng the whole first equation through by 5.\r\n" );
document.write( "2. We need to make the -5 in the second into a +15 \r\n" );
document.write( "by multiplyng the whole second equation through by -3.\r\n" );
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document.write( " (5)2x -  (5)3y =  (5)(-5)\r\n" );
document.write( "(-3)3x - (-3)5y = (-3)(-9)\r\n" );
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document.write( "which when simplified becomes:\r\n" );
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document.write( "     10x - 15y = -25\r\n" );
document.write( "     -9x + 15y =  27\r\n" );
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document.write( "Add term by term vertically\r\n" );
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document.write( "    10x - 15y = -25\r\n" );
document.write( "    -9x + 15y =  27\r\n" );
document.write( "   ------------------\r\n" );
document.write( "      x       =   2\r\n" );
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document.write( "Substitute 2 for x in\r\n" );
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document.write( "   2x - 3y = -5\r\n" );
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document.write( " 2(2) - 3y = -5\r\n" );
document.write( "    4 - 3y = -5\r\n" );
document.write( "       -3y = -5 - 4\r\n" );
document.write( "       -3y = -9\r\n" );
document.write( "          y = (-9)/(-3)\r\n" );
document.write( "          y = 3\r\n" );
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document.write( "So the solution is (x,y) = (2,3).\r\n" );
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document.write( "Edwin
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