document.write( "Question 66010: Solve the following system of equations algebraically:
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Algebra.Com's Answer #46739 by Edwin McCravy(20054) $\"\"$ $\"About$
You can put this solution on YOUR website!
Solve the following system of equations\r\n" );
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document.write( "9x² + y² = 9\r\n" );
document.write( "  3x – y = 3\r\n" );
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document.write( "Let's do it algebraically and then check it\r\n" );
document.write( "graphically:\r\n" );
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document.write( "Solve the second equation for y\r\n" );
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document.write( "  3x – y = 3\r\n" );
document.write( "      -y = 3 - 3x\r\n" );
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document.write( "Multiply through by -1\r\n" );
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document.write( "       y = -3 + 3x\r\n" );
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document.write( "Save one sign by swapping terms\r\n" );
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document.write( "       y = 3x - 3\r\n" );
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document.write( "Substitute into the 1st equation:\r\n" );
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document.write( "               9x² + y² = 9\r\n" );
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document.write( "        9x² + (3x - 3)² = 9\r\n" );
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document.write( " 9x² + (3x - 3)(3x - 3) = 9\r\n" );
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document.write( "9x² + 9x² - 9x - 9x + 9 = 9\r\n" );
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document.write( "         18x² - 18x + 9 = 9\r\n" );
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document.write( "             18x² - 18x = 0\r\n" );
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document.write( "Factor out 18x\r\n" );
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document.write( "             18x(x - 1) = 0\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "18x = 0 gives x = 0\r\n" );
document.write( "x - 1 = 0 gives x = 1\r\n" );
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document.write( "For each of those solutions for x,\r\n" );
document.write( "we must find a corresponding solution\r\n" );
document.write( "for y:\r\n" );
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document.write( "To find this we substitute into\r\n" );
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document.write( "         y = 3x - 3 \r\n" );
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document.write( "For x = 0,\r\n" );
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document.write( "         y = 3(0) - 3\r\n" );
document.write( "         y = -3\r\n" );
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document.write( "So one solution is (x, y) = (0, -3)\r\n" );
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document.write( "For x = 1,\r\n" );
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document.write( "         y = 3(1) - 3\r\n" );
document.write( "         y = 0\r\n" );
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document.write( "So the other solution is (x, y) = (1, 0)\r\n" );
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document.write( "This means the two graphs would have\r\n" );
document.write( "two points of intersection. The graph of\r\n" );
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document.write( "9x² + y² = 9\r\n" );
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document.write( "is this oval shaped graph, called an\r\n" );
document.write( "ellipse:\r\n" );
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document.write( "and the graph of 3x – y = 3\r\n" );
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document.write( "is this line which crosses it twice:\r\n" );
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document.write( "Notice that the graphs cross at the points (1, 0)\r\n" );
document.write( "and (0, -3)\r\n" );
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document.write( "Edwin
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