document.write( "Question 1195199: Solve the equation
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Algebra.Com's Answer #827614 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Left side is\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Right side is\r\n" );
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document.write( "    216 =  = .\r\n" );
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document.write( "So, equation is\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Due to uniqueness of the decomposition of integer numbers into the product of primes, it implies\r\n" );
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document.write( "    2x + 3y = 3,    (1)\r\n" );
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document.write( "     x +  y = 3.    (2)\r\n" );
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document.write( "So, we have a system of two equations.\r\n" );
document.write( "It can be easily solved by Substitution or by Elimination.\r\n" );
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document.write( "Let's do it using substitution x = 3 - y from equation (2).\r\n" );
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document.write( "Then equation (1) will give you\r\n" );
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document.write( "    2(3-y) + 3y = 3\r\n" );
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document.write( "    6 - 2y + 3y = 3\r\n" );
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document.write( "           y    = 3 - 6 = -3.\r\n" );
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document.write( "Then from (2),  x = 3 - y = 3 - (-3) = 6.\r\n" );
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document.write( "ANSWER.  x = 6,  y = -3.\r\n" );
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document.write( "You can make check on your own to convince yourself that the answer is correct.\r\n" );
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document.write( "    //  I did such check for myself.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Addition made after reading the post by Alan.\r
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document.write( "    Alan made right notice that in the form, as the problem is worded, printed, posted and presented, \r\n" );
document.write( "    it has infinitely many solutions in real numbers x, y.\r\n" );
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document.write( "    But, surely, the meaning of the problem is different, and in order for the meaning was restored,\r\n" );
document.write( "    the problem's formulation should be changed.\r\n" );
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document.write( "    The correct problem's formulation is\r\n" );
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document.write( "      +------------------------------------------------------------------------+\r\n" );
document.write( "      | Find solution/solutions of equation  12^x*24^y=216  in integer numbers.|\r\n" );
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document.write( "    In this form, my solution above works and produces a unique answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Alan, thanks for your notice.\r
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