\r\n" );
document.write( "x^1/2 + y = 7\r\n" );
document.write( "x + y^1/2 = 11\r\n" );
document.write( "Find the value of x and y\r\n" );
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____
\r\n" );
document.write( " 
\r\n" );
document.write( " 
\r\n" );
document.write( " 
----- eq (i)\r\n" );
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document.write( " 
\r\n" );
document.write( " 
----- eq (ii)\r\n" );
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document.write( "We then get: 
\r\n" );
document.write( " 
\r\n" );
document.write( " 
\r\n" );
document.write( "\r\n" );
document.write( " Let 
\r\n" );
document.write( " Then: 
\r\n" );
document.write( " then becomes: \r\n" );
document.write( " 
\r\n" );
document.write( " 
\r\n" );
document.write( "Using the RATIONAL ROOT THEOREM, we find that a root of the above equation is: t = 2, which makes its\r\n" );
document.write( "FACTOR, t - 2. When divided by t - 2, using LONG DIVISION of POLYNOMIALS, or using SYNTHETIC DIVISION,\r\n" );
document.write( "the other factor of 
, besides t - 2, is: 
.\r\n" );
document.write( "From this, we find another REAL solution being approximately 3.13131. The other 2 are negative (< 0) and\r\n" );
document.write( "so, MUST be REJECTED/IGNORED, since CANNOT have a negative (< 0) value for t. \r\n" );
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document.write( "I will continue with the REAL INTEGER value, 2.\r\n" );
document.write( " 
---- Back-substituting t = 2 for 
\r\n" );
document.write( "
\r\n" );
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document.write( " ----- eq (ii)\r\n" );
document.write( " x = 11 - 2 ----- Substituting 2 for in eq (ii)\r\n" );
document.write( " x = 9\r\n" );
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document.write( "So, the ONLY INTEGER-solution set is: (x, y) = (9, 4). I'll let you substitute the other REAL VALUE, 3.13131\r\n" );
document.write( "for t, to determine the other SOLUTION-SET.
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
