document.write( "Question 41907: USE LINEAR COMBINATIONS TO SOLVE THE LINEAR EQUATIONS\r
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\n" ); document.write( "\n" ); document.write( "1. X+ 2Y =5
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\n" ); document.write( "\n" ); document.write( "2. x + Y =1
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\n" ); document.write( "\n" ); document.write( "3. x - y = -4
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Algebra.Com's Answer #27028 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
USE LINEAR COMBINATIONS TO SOLVE THE LINEAR EQUATIONS \r\n" );
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document.write( "1.\r\n" );
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document.write( "   x + 2y = 5\r\n" );
document.write( "  3x - 2y = 7 \r\n" );
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document.write( "Since the coefficients of y are already equal in\r\n" );
document.write( "absolute value but opposite in sign, we can add\r\n" );
document.write( "1 times the first to 1 times the second and the\r\n" );
document.write( "y terms will cancel\r\n" );
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document.write( " 1(  x + 2y = 5)\r\n" );
document.write( " 1( 3x - 2y = 7)\r\n" );
document.write( "覧覧覧覧覧覧覧覧\r\n" );
document.write( "    4x      = 12\r\n" );
document.write( "          x = 3\r\n" );
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document.write( "Then substitute to find y:\r\n" );
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document.write( "     x + 2y = 5\r\n" );
document.write( "   (3) + 2y = 5\r\n" );
document.write( "         2y = 5 - 3\r\n" );
document.write( "         2y = 2\r\n" );
document.write( "          y = 1\r\n" );
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document.write( "2.    x +  y =  1\r\n" );
document.write( "     2x - 3y = 12 \r\n" );
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document.write( "Multiply the 1st equation by 3\r\n" );
document.write( "Multiply the second by 1\r\n" );
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document.write( "  3[  x +  y =  1]\r\n" );
document.write( "  1[ 2x - 3y = 12]\r\n" );
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document.write( "     3x + 3y =  3\r\n" );
document.write( "     2x - 3y = 12\r\n" );
document.write( "    覧覧覧覧覧覧予r\n" );
document.write( "     5x      = 15\r\n" );
document.write( "           x = 3\r\n" );
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document.write( "Then substitute to find y\r\n" );
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document.write( "       x + y = 1\r\n" );
document.write( "       3 + y = 1\r\n" );
document.write( "           y = -2\r\n" );
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document.write( "3. x -  y = -4\r\n" );
document.write( "   x + 2y = 5\r\n" );
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document.write( "Multiply the first equation by 2 and the second\r\n" );
document.write( "by 1 to make the y's cancel out:\r\n" );
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document.write( "2[x -  y = -4]\r\n" );
document.write( "1[x + 2y =  5]\r\n" );
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document.write( "  2x - 2y = -8\r\n" );
document.write( "   x + 2y =  5\r\n" );
document.write( " 覧覧覧覧覧覧予r\n" );
document.write( "  3x      = -3\r\n" );
document.write( "        x = -1 \r\n" );
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document.write( "Substitute to find y\r\n" );
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document.write( "  x + 2y = 5\r\n" );
document.write( " -1 + 2y = 5\r\n" );
document.write( "      2y = 6\r\n" );
document.write( "       y = 3\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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