document.write( "Question 1183898: What should be the value(s) of k so that the system \r
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Algebra.Com's Answer #814386 by ikleyn(52793) $\"\"$ $\"About$

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document.write( "If the determinant of the coefficient matrix is not zero, then the system IS CONSISTENT.\r\n" );
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document.write( "Hence, the only case, when it can be inconsistent, is equality of the determinant to zero.\r\n" );
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document.write( "It gives  2*3 - (-5)*k = 0,  or  6 + 5k = 0,   5k = -6,   k =  = -1.2.\r\n" );
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document.write( "With this value of k, the system takes the form\r\n" );
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document.write( "     2x   - 5y = -1.2      (1)\r\n" );
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document.write( "    -1.2x + 3y =  1        (2)\r\n" );
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document.write( "To convince yourself that it is INCONSISTENT, multiply equation (1) by 3; multiply equation (2) by -5.\r\n" );
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document.write( "You will get then the EQUIVALENT system\r\n" );
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document.write( "    6x - 15y = -3.6     (3)\r\n" );
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document.write( "    6x - 15y =  -5.     (4)\r\n" );
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document.write( "Comparing equations (3) and (4), you see that their left sides are IDENTICAL, \r\n" );
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document.write( "while their right sides are DIFFERENT.\r\n" );
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document.write( "It shows that the system (3), (4) is INCOMPATIBLE  (= inconsistent).\r\n" );
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document.write( "With it, the equivalent system (1), (2) is inconsistent, too.\r\n" );
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