document.write( "Question 1208978: 3x + 2y = 19
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Algebra.Com's Answer #847528 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Your starting equations are\r\n" );
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document.write( "    3x + 2y = 19,    (1)\r\n" );
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document.write( "    xy = 15.         (2)\r\n" );
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document.write( "From equation (1),  express  2y = 19-3x.\r\n" );
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document.write( "Write equation (2) in the form\r\n" );
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document.write( "    2xy = 30,  or  x*(2y) = 30,   and replace there 2y by 19-3x.\r\n" );
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document.write( "You will get\r\n" );
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document.write( "    x*(19-3x) = 30.\r\n" );
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document.write( "Reduce to the standard form quadratic equation\r\n" );
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document.write( "    19x - 3x^2 = 30,\r\n" );
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document.write( "    3x^2 - 19x + 30 = 0.    (3)\r\n" );
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document.write( "Calculate the discriminant  d = b^2 - 4ac = (-19)^2 - 4*3*30 = 1\r\n" );
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document.write( "and apply the quadratic formula\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "The solutions for x are  \r\n" );
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document.write( "     =  =  = ;\r\n" );
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document.write( "     =  =  = 3.\r\n" );
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document.write( "If  x= ,  then  2y = 19-3x =  = 19 - 10 = 9,  so  y = .\r\n" );
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document.write( "If  x= 3,  then  2y = 19-3x =  = 19 - 9 = 10,  so  y =  = 5.\r\n" );
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document.write( "ANSWER.  The system of the given equations has two solutions:\r\n" );
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document.write( "         (x,y) = (,)  and  (x,y) = (3,5).\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from my post:\r
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\n" ); document.write( "\n" ); document.write( " Notice how I have, not without grace, carried out \r
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\n" ); document.write( "\n" ); document.write( "If you demonstrate this trick in front of your Math teacher,
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