document.write( "Question 1182622: please help me solve \r
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Algebra.Com's Answer #812706 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Your starting equations are\r\n" );
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document.write( "    25x^2 - y^2 = 36      (1)\r\n" );
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document.write( "    5x    + y   =  2      (2)\r\n" );
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document.write( "This system of two equations (one equation of the degree 2 and the other of the degree 1) is very special.\r\n" );
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document.write( "Although one of the starting equations is of the degree 2, the system can be reduced to the system \r\n" );
document.write( "of two LINEAR equations, which can be EASILY solved.\r\n" );
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document.write( "The first equation admits factoring\r\n" );
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document.write( "    (5x - y)*(5x + y) = 36    (3)\r\n" );
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document.write( "In this factored equation, we can replace (5x + y) by the value of 2, based on equation (2).\r\n" );
document.write( "Doing it, we transform equation (3) to the form\r\n" );
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document.write( "    2*(5x - y) = 36,  \r\n" );
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document.write( "or\r\n" );
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document.write( "    5x - y = 18             (4)\r\n" );
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document.write( "(where 18 = 36/2).\r\n" );
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document.write( "Thus from the original non-linear system of equation, we get the linear system\r\n" );
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document.write( "    5x - y = 18             (4)\r\n" );
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document.write( "    5x + y =  2             (5)\r\n" );
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document.write( "The system of linear equations (4), (5) is EQUIVALENT to the nonlinear system of equations (1), (2).\r\n" );
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document.write( "To solve equations (4), (5), use the ELIMINATION method and add equations (4) and (5).  You will get\r\n" );
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document.write( "    10x = 18 + 2 = 20\r\n" );
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document.write( "      x          = 20/10 = 2.\r\n" );
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document.write( "To find y, substitute the found value x= 2 into equation (5).  You will get\r\n" );
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document.write( "    5*2 + y = 2,  y = 2 - 10 = -8.\r\n" );
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document.write( "Thus the original system of equations (1), (2) has a UNIQUE solution (x,y) = (2,-8).\r\n" );
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\n" ); document.write( "\n" ); document.write( "The fact that the solution is unique  tells  us  that the straight line,  defined by equation  (2), \r
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