document.write( "Question 1049435: The distinct real numbers x and y satisfy x^2=33y+907 and y^2=33x+907. Find x and y. \n" ); document.write( "

Algebra.Com's Answer #665039 by ikleyn(52866) $\"\"$ $\"About$

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\n" ); document.write( "The distinct real numbers x and y satisfy x^2=33y+907 and y^2=33x+907. Find x and y.
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document.write( "x^2 = 33y + 907,   (1)\r\n" );
document.write( "y^2 = 33x + 907.   (2)\r\n" );
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document.write( "Distract eq.(2) from eq.(1) (both sides). You will get\r\n" );
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document.write( "x^2 - y^2 = 33y - 33x,   or\r\n" );
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document.write( "(x-y)*(x+y) = -33(x-y).\r\n" );
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document.write( "Since the numbers are distinct, you can divide both sides of the last equation by (x-y). Then you get\r\n" );
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document.write( "x + y = -33.        (3)\r\n" );
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document.write( "Now express  x = -33-y from (3) and substitute it into (2). You will get\r\n" );
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document.write( "y^2 = 33(-33-y) + 907,   or\r\n" );
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document.write( "y^2 + 33y + 182 = 0.\r\n" );
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document.write( "Solve this quadratic equation using the quadratic formula.\r\n" );
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document.write( " =  = ,\r\n" );
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document.write( " = -7,   = -26.\r\n" );
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document.write( "Correspondingly, there are two solutions for x:\r\n" );
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document.write( " = -33 - (-7) = -33 + 7 = -26,  and   = -33  (-26) = -33 + 26 = -7.\r\n" );
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document.write( "Answer.  The solutions are (x,y) = (-7,-26)  or/and (-26,-7).\r\n" );
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