document.write( "Question 38924: what is the point of intersection of the following systems of equations algebraically?
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Algebra.Com's Answer #24375 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
What is the point of intersection of the following \r\n" );
document.write( "systems of equations algebraically?\r\n" );
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document.write( "      xy = 8\r\n" );
document.write( "   x + y = 6\r\n" );
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document.write( "Method: substitution.\r\n" );
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document.write( "Solve the second equation for y\r\n" );
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document.write( "       y = 6 - x\r\n" );
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document.write( "Substitute (6 - x) for y in the first equation\r\n" );
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document.write( "      xy = 8\r\n" );
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document.write( "x(6 - x) = 8\r\n" );
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document.write( " 6x - x² = 8\r\n" );
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document.write( "Get 0 on the left\r\n" );
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document.write( "       0 = x² - 6x + 8\r\n" );
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document.write( "       0 = (x - 2)(x - 4)\r\n" );
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document.write( "Use the zero-factor property\r\n" );
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document.write( "x - 2 = 0 gives x = 2\r\n" );
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document.write( "x - 4 = 0 gives x = 4\r\n" );
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document.write( "There are two values for x.\r\n" );
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document.write( "For each of these two values for x, we must\r\n" );
document.write( "find a corresponding value for y.  We use\r\n" );
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document.write( "       y = 6 - x\r\n" );
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document.write( "To find the y-value that corresponds to x = 2\r\n" );
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document.write( "       y = 6 - 2\r\n" );
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document.write( "       y = 4\r\n" );
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document.write( "So one solution is the point (x, y) = (2, 4)\r\n" );
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document.write( "To find the y-value that corresponds to x = 4\r\n" );
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document.write( "       y = 6 - 4\r\n" );
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document.write( "       y = 2\r\n" );
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document.write( "So the other solution is the point (x, y) = (4, 2)\r\n" );
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document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
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