document.write( "Question 1063521: Find the value of K for the followibg pair of linear equation have infinetly many solution :—
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Algebra.Com's Answer #678649 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "Find the value of K for the following pair of linear equation have infinitely many solution :—
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document.write( "x      + (k+1)y = 5,         (1)\r\n" );
document.write( "(k+1)x +     9y = 8y - 1.    (2)\r\n" );
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document.write( "is equivalent to \r\n" );
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document.write( "x      + (k+1)y =  5,        (1')\r\n" );
document.write( "(k+1)x +      y = -1.        (2')\r\n" );
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document.write( "The theory says: \r\n" );
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document.write( "   - if the determinant of the matrix of the system is not zero, then the solution is unique.\r\n" );
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document.write( "   - if the determinant of the matrix of the system is zero,     then two options are possible: \r\n" );
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document.write( "     1) there is NO solution,  OR  2) there are infinitely many solutions.\r\n" );
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document.write( "The determinant of the matrix is\r\n" );
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document.write( "     det  =  = .\r\n" );
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document.write( "The condition det = 0 is this equation for \"k\"\r\n" );
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document.write( " = 1,\r\n" );
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document.write( "which has these two solutions:   = 0,    = -2.\r\n" );
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document.write( "At k = 0 the system (1'), (2') is \r\n" );
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document.write( " x + y =  5,     \r\n" );
document.write( " x + y = -1\r\n" );
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document.write( "and has NO solutions. \r\n" );
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document.write( "At k = -2 the system (1'), (2') is \r\n" );
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document.write( " x - y =  5,     \r\n" );
document.write( "-x + y = -1\r\n" );
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document.write( "and has NO solutions, again. \r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. There is NO value of \"k\" such that the original system has infinitely many solutions.\r
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