document.write( "Question 143429: Determine the augmented matrix:p+s+c=600; 12p+10s+8c=5900; 0-s+c=175\r
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Algebra.Com's Answer #104487 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Determine the augmented matrix:p+s+c=600; 12p+10s+8c=5900; 0-s+c=175
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document.write( "\"++p%2B++s%2B+c+=+++600\"\r\n" );
document.write( "\"12p%2B10s%2B8c+=+5900\"\r\n" );
document.write( "\"0++-s%2B+c+=++175\" \r\n" );
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document.write( "Solve for the matrix and please show all work. \r\n" );
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document.write( "Put in all the \"1\" coefficients and make the \"0\" a \"0p\"\r\n" );
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document.write( "\"1p%2B1s%2B1c=600\"\r\n" );
document.write( "\"12p%2B10s%2B8c=5900\"\r\n" );
document.write( "\"0p-1s%2B1c=175\"\r\n" );
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document.write( "Now erase all the letters and you have\r\n" );
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document.write( "The idea is to get three \"0\"'s in the lower left corner:\r\n" );
document.write( "Multiply the top row through by -12\r\n" );
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document.write( "Add the top row to the middle row:\r\n" );
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document.write( "Restore the top row\r\n" );
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document.write( "Multiply the bottom row by -2\r\n" );
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document.write( "Add the middle row to the bottom row:\r\n" );
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document.write( "Now we've gotten three \"0\"'s in the bottom left.\r\n" );
document.write( "So we make the matrix back into 3 equations:\r\n" );
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document.write( "\"1p%2B1s%2B1c=600\"\r\n" );
document.write( "\"0p-2s-4c=-1300\"\r\n" );
document.write( "\"0p%2B0s-6c=-1650\"\r\n" );
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document.write( "Drop the 0 terms and make the 1's invisible:\r\n" );
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document.write( "\"p%2Bs%2Bc=600\"\r\n" );
document.write( "\"-2s-4c=-1300\"\r\n" );
document.write( "\"-6c=-1650\"\r\n" );
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document.write( "Solve from the bottom to top.\r\n" );
document.write( "Solve the bottom equation for \"c\"\r\n" );
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document.write( "\"-6c=-1650\"\r\n" );
document.write( "\"%28-6c%29%2F%28-6%29=%28-1650%29%2F%28-6%29\"\r\n" );
document.write( "\"c=275\"\r\n" );
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document.write( "Plug that into the second equation:\r\n" );
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document.write( "\"-2s-4c=-1300\"\r\n" );
document.write( "\"-2s-4%28275%29=-1300\"\r\n" );
document.write( "\"-2s-1100=-1300\"\r\n" );
document.write( "\"-2s=-200\"\r\n" );
document.write( "\"%28-2s%29%2F%28-2%29=%28-200%29%2F%28-2%29\"\r\n" );
document.write( "\"s=100\"\r\n" );
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document.write( "Plug that and \"c=275\" into the first\r\n" );
document.write( "equation:\r\n" );
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document.write( "\"p%2Bs%2Bc=600\"\r\n" );
document.write( "\"p%2B100%2B275=600\"\r\n" );
document.write( "\"p%2B375=600\"\r\n" );
document.write( "\"p=225\"\r\n" );
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document.write( "So\r\n" );
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document.write( "(\"p\",\"s\",\"c\") = (\"225\",\"100\",\"275\")\r\n" );
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document.write( "Edwin
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