document.write( "Question 69844: Solve the system by addition.
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Algebra.Com's Answer #49754 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "To find y we eliminate x:\r\n" );
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document.write( "To eliminate the x terms, look at the coefficients\r\n" );
document.write( "of x:\r\n" );
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document.write( "2x – 4y = 7\r\n" );
document.write( "4x + 2y = 9\r\n" );
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document.write( "They are 2 and 4.   Their least common multiple in\r\n" );
document.write( "absolute value is 4. Multiply the first equation \r\n" );
document.write( "through by -2 to make the 2x become -4x, so it will \r\n" );
document.write( "cancel with the 4x in the second equation:\r\n" );
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document.write( "-2[2x - 4y = 7]\r\n" );
document.write( "   4x + 2y = 9 \r\n" );
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document.write( "  -4x + 8y = -14\r\n" );
document.write( "   4x + 2y =   9\r\n" );
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document.write( "Now add vertically term-by-term:\r\n" );
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document.write( "  -4x + 8y = -14\r\n" );
document.write( "   4x + 2y =   9\r\n" );
document.write( "       10y =  -5\r\n" );
document.write( "         y = -5/10\r\n" );
document.write( "         y = -1/2\r\n" );
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document.write( "\r\n" );
document.write( "To find x we eliminate y:\r\n" );
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document.write( "To eliminate the y terms, look at the coefficients\r\n" );
document.write( "of y:\r\n" );
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document.write( "2x – 4y = 7\r\n" );
document.write( "4x + 2y = 9\r\n" );
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document.write( "They are -4 and 2.   Their least common multiple in\r\n" );
document.write( "absolute value is 4. Multiply the second equation \r\n" );
document.write( "through by 2 to make the 2y become 4y, so it will \r\n" );
document.write( "cancel with the -4y in the first equation:\r\n" );
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document.write( "   2x - 4y = 7\r\n" );
document.write( " 2[4x + 2y = 9] \r\n" );
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document.write( "   2x - 4y =  7\r\n" );
document.write( "   8x + 4y = 18\r\n" );
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document.write( "Now add vertically term-by-term:\r\n" );
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document.write( "   2x - 4y =  7\r\n" );
document.write( "   8x + 4y = 18\r\n" );
document.write( "  10x      = 25\r\n" );
document.write( "         x = 25/10\r\n" );
document.write( "         x = 5/2\r\n" );
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document.write( "So the solution is (x,y) = (5/2,-1/2) \r\n" );
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document.write( "Edwin

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