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document.write( "To do this efficiently you need something like a not too old TI-84 \r\n" );
document.write( "calculator, and to learn how to store a number for a letter, and \r\n" );
document.write( "how to scroll up to bring back expressions you have previously used, \r\n" );
document.write( "so you won't have to type them in but once.\r\n" );
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document.write( "
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document.write( "Rearrange the equations, if possible, so that \r\n" );
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document.write( "1. the equation that comes 1st is one which has its \r\n" );
document.write( "x-coefficient greater in absolute value than either \r\n" );
document.write( "its y-coefficient or its z-coefficient.\r\n" );
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document.write( "2. the equation that comes 2nd is one which has its \r\n" );
document.write( "y-coefficient greater in absolute value than either \r\n" );
document.write( "its x-coefficient or its z-coefficient. \r\n" );
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document.write( "3. the equation that comes 3rd is one which has its \r\n" );
document.write( "z-coefficient greater in absolute value than either \r\n" );
document.write( "its x-coefficient or its y-coefficient.\r\n" );
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document.write( "In other words, the largest coefficient in each equation\r\n" );
document.write( "is on the diagonal.\r\n" );
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document.write( "Solve the first for x, the second for y, and the third for z\r\n" );
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document.write( "Iteration| x | y | z | \r\n" );
document.write( " 1 | 0.0000| 0.0000| 0.0000| \r\n" );
document.write( " 2 | 0.7143|-1.9429| 3.4357|\r\n" );
document.write( " 3 | 0.7786|-3.3300| 4.0811|\r\n" );
document.write( " 4 | 1.0827|-3.6490| 4.0125|\r\n" );
document.write( " 5 | 1.1836|-3.6417| 3.9331|\r\n" );
document.write( " 6 | 1.1848|-3.6011| 3.9120|\r\n" );
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document.write( "Start out with all 0's for the first iteration.\r\n" );
document.write( "Substitute (x,y,z)=(0,0,0) in the equation for x, get x=0.7143.\r\n" );
document.write( "Substitute (x,y,z)=(0.7143,0,0) in the equation for y, get y=-1.9429.\r\n" );
document.write( "Substitute (x,y,z)=(0.7143,-1.9429,0) in the equation for z, get z=-3.4357.\r\n" );
document.write( "That's the end of the 2nd iteration. Now we begin the 3rd iteration.\r\n" );
document.write( "Substitute (x,y,z)=(0.7143,-1.9429,-3.4357) in the equation for x, \r\n" );
document.write( "get 0.7786.\r\n" );
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document.write( "etc., etc.\r\n" );
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document.write( "The actual solution using the methods of 2nd year algebra, gives:\r\n" );
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document.write( "
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document.write( "You can see that the iterations are getting closer and closer to\r\n" );
document.write( "the actual solutions.\r\n" );
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
