document.write( "Question 1199804: Using graphical method, please solve
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Algebra.Com's Answer #833770 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " Graphical method is irrelevant in this problem.\r
\n" ); document.write( "\n" ); document.write( " It is intended to be solved by the pure Algebra method.\r
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document.write( "Your starting system of equations is\r\n" );
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document.write( "    4x^2 - y^2 = 15       (1)\r\n" );
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document.write( "     2x  - y   = 5        (2)\r\n" );
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document.write( "Decompose first equation as the difference of squares\r\n" );
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document.write( "    (2x-y)*(2x+y) = 15    (3)\r\n" );
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document.write( "In this equation, replace (2x-y) by 5, based on equation (2)\r\n" );
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document.write( "    5*(2x+y) = 15\r\n" );
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document.write( "which gives\r\n" );
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document.write( "    2x + y = 15/5 = 3.\r\n" );
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document.write( "So, now you have two linear equations instead of (1) and (2)\r\n" );
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document.write( "    2x + y = 3    (4)\r\n" );
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document.write( "    2x - y = 5    (5)\r\n" );
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document.write( "To solve, add the equations.  You will get\r\n" );
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document.write( "    4x = 3 + 5 = 8,  hence  x = 8/4 = 2.\r\n" );
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document.write( "Then from equation (3)\r\n" );
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document.write( "    y = 3 - 2x = 3 - 2*2 = -1.\r\n" );
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document.write( "ANSWER.  x = 2;  y = -1.\r\n" );
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