document.write( "Question 987450: 7x+3y+6z=-7
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\n" ); document.write( "for the system to be consistent we must have k≠? \n" ); document.write( "
Algebra.Com's Answer #608441 by Edwin McCravy(20056)\"\" \"About 
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document.write( " 7x +  3y +  6z =  -7\r\n" );
document.write( "-7x +  8y +  kz =  -4\r\n" );
document.write( " 7x + 25y + 28z = -30\r\n" );
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document.write( "Add the 1st and 2nd equations:\r\n" );
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document.write( " 7x +  3y +     6z =  -7\r\n" );
document.write( "-7x +  8y +     kz =  -4\r\n" );
document.write( "------------------------\r\n" );
document.write( "      11y + (6+k)z = -11        <--- equation A\r\n" );
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document.write( "Add the 2nd and 3rd equations:\r\n" );
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document.write( "-7x +  8y +      kz =  -4\r\n" );
document.write( " 7x + 25y +     28z = -30\r\n" );
document.write( "-------------------------\r\n" );
document.write( "      33y + (k+28)z = -34       <--- equation B\r\n" );
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document.write( "Multiply equation A by -3 and add it to equation B\r\n" );
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document.write( "      -33y -       3(6+k)z =  33       <--- -3 times equation A\r\n" );
document.write( "       33y +       (k+28)z = -34       <--- equation B\r\n" );
document.write( "--------------------------------\r\n" );
document.write( "          [-3(6+k)+(k+28]z =  -1\r\n" );
document.write( "            [-18-3k+k+28]z =  -1\r\n" );
document.write( "                  [10-2k]z =  -1\r\n" );
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document.write( "It will be consisitent if and only if the coefficient of z is not 0\r\n" );
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document.write( "                     10-2k ≠ 0\r\n" );
document.write( "                       -2k ≠ -10\r\n" );
document.write( "                         k ≠ 5                         \r\n" );
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document.write( "Edwin
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