document.write( "Question 1100656: In the system shown below, what are the coordinates of the solution that lies in quadrant II? Write our answer in the form (a,b) without using spaces. x^2+y^2=5 y=1/4x^2
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Algebra.Com's Answer #715175 by ikleyn(52835) $\"\"$ $\"About$

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document.write( "x^2 + y^2 = 5        (1)\r\n" );
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document.write( "y = (1/4)*x^2        (2)\r\n" );
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document.write( "From eq(2) express x^2 = 4y.  Next, replace x^2 in the eq(1) by 4y, based on it.\r\n" );
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document.write( "You will get a single equation for the unknown y:\r\n" );
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document.write( "4y^2 + y^2 = 5  ====>  5y^2 = 5  ====>  y^2 = 1  ====>  y = +/- 1/\r\n" );
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document.write( "Since  y = (1/4)*x*2, y can not be negative; hence the solution y = -1 does not work,  and we actually have only ONE solution y = 1\r\n" );
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document.write( "If y = 1 then  x^2 + 1^2 = 5  ====>  x^2 = 5-1 = 4  ====>  x = +/- 2.\r\n" );
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document.write( "Thus you have TWO solutions for the original system:  (2,1) and (-2,1).\r\n" );
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document.write( "Of them, only the solution (-2,1) lies in QII.\r\n" );
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