document.write( "Question 1178359: Solve y=1/x and x^2+y^2=2 simultaneously.
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Algebra.Com's Answer #807594 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Our starting equations are\r\n" );
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document.write( "    x^2 + y^2 = 2      (1)\r\n" );
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document.write( "    y =              (2)\r\n" );
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document.write( "From equation (2),  \r\n" );
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document.write( "    xy = 1             (3)\r\n" );
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document.write( "So, I will multiply equation (3) by 2 (both sides) and then subtract it from equation (1).  I will get then\r\n" );
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document.write( "    x^2 - 2xy + y^2 = 0,\r\n" );
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document.write( "or\r\n" );
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document.write( "    (x-y)^2 = 0.\r\n" );
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document.write( "It means  x = y,  and then from equation (1) I have\r\n" );
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document.write( "    2x^2 = 2,  x^2 = 1, x = +/- 1.\r\n" );
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document.write( "Thus the two solutions are  \r\n" );
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document.write( "    x = y = 1   and/or   x = y = -1.\r\n" );
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