document.write( "Question 1131189: The difference between the squares of two numbers is 15. Four times the square of the first number increased by the square of the second number is 65. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #747808 by ikleyn(52835) $\"\"$ $\"About$

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document.write( " x^2 - y^2 = 15     (1)\r\n" );
document.write( "4x^2 + y^2 = 65.    (2)\r\n" );
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document.write( "------------------------ Add the equations.  In this way you eliminate y^2 \r\n" );
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document.write( "5x^2 = 15 + 65,\r\n" );
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document.write( "5x^2 = 80,\r\n" );
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document.write( "x^2 = 80/5 = 16  ====>  x = +/-  = +/- 4.\r\n" );
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document.write( "Then from eq(1),  y^2 = x^2 - 15 = 16 - 15 = 1  ====>  y = +/-  = +/- 1.\r\n" );
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document.write( "Answer.  The numbers are  (4,1),  (-4,1),  (4,-1)  and  (-4,-1).  In all, there are 4 solutions.\r\n" );
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