document.write( "Question 108983: Solve each of the following systems by graphing.
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Algebra.Com's Answer #79495 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Solve each of the following systems by graphing.\r\n" );
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document.write( "2x - y = 4\r\n" );
document.write( "2x - y = 6\r\n" );
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document.write( "Get two points on the first line.\r\n" );
document.write( "Plot them and draw a line through them.\r\n" );
document.write( "Get two points on the second line.\r\n" );
document.write( "Plot them and draw a line through them.\r\n" );
document.write( "Identify the coodinates of the point where the two lines cross.\r\n" );
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document.write( "Get two points on the first line whose equation is  2x - y = 4\r\n" );
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document.write( "Arbitrarily pick any convenient number to substitute\r\n" );
document.write( "for either letter.  I think I will first choose 0 to substitute\r\n" );
document.write( "for x.  I chose 0 simply because it is easy.  I could have chosen\r\n" );
document.write( "any other number, and for either letter.  So we substitute x = 0\r\n" );
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document.write( "  2x - y = 4\r\n" );
document.write( "2(0) - y = 4\r\n" );
document.write( "   0 - y = 4\r\n" );
document.write( "      -y = 4\r\n" );
document.write( "     -1y = 4\r\n" );
document.write( "      y = \"4%2F%28-1%29\" \r\n" );
document.write( "      y = -4, so one point on the first line is (x, y) = (0,-4) \r\n" );
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document.write( "Now for the second point on the first line, I think I will choose 0 to substitute for y.  Again I chose 0 simply because it is easy.  I could \r\n" );
document.write( "have chosen any other number, and for either letter.  So we substitute\r\n" );
document.write( "y = 0\r\n" );
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document.write( "  2x - y = 4\r\n" );
document.write( " 2x -(0) = 4\r\n" );
document.write( "      2x = 4\r\n" );
document.write( "       x = \"4%2F2\"\r\n" );
document.write( "       x = 2, so another point on the first line is (x, y) = (2, 0)\r\n" );
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document.write( "Plot the two points (0, -4) and (2, 0):\r\n" );
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document.write( "Draw a straight line through them:\r\n" );
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document.write( "Get two points on the second line, whose equation is 2x - y = 6\r\n" );
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document.write( "Arbitrarily pick any convenient number to substitute\r\n" );
document.write( "for either letter.  I will again first choose 0 to substitute\r\n" );
document.write( "for x.  Again I chose 0 simply because it is easy.  I could have chosen\r\n" );
document.write( "any other number, and for either letter.  So we substitute x = 0\r\n" );
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document.write( "  2x - y = 6\r\n" );
document.write( "2(0) - y = 6\r\n" );
document.write( "      -y = 6\r\n" );
document.write( "       y = \"6%2F%28-1%29\"\r\n" );
document.write( "       y = -6, so another point on the second line is (x, y) = (0, -6) \r\n" );
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document.write( "Now for the second point on the second line, I will again choose 0 to\r\n" );
document.write( "substitute for y.  Again I chose 0 simply because it is easy.  I could \r\n" );
document.write( "have chosen any other number, and for either letter.  So we substitute\r\n" );
document.write( "y = 0\r\n" );
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document.write( "  2x - y = 6\r\n" );
document.write( " 2x -(0) = 6\r\n" );
document.write( "      2x = 6\r\n" );
document.write( "       x = \"6%2F2\"\r\n" );
document.write( "       x = 3, so another point on the first line is (x, y) = (3, 0)\r\n" );
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document.write( "Plot the two points (0, -4) and (3, 0):\r\n" );
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document.write( "so another point on the second line is (x, y) = (4, 0)\r\n" );
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document.write( "Plot the two points (0, -6) and (3, 0):\r\n" );
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document.write( "Draw a straight line through them:\r\n" );
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document.write( "Oh,oh!  These two lines are parallel and therefore\r\n" );
document.write( "they do not intersect, so there is no solution.\r\n" );
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document.write( "This type of system is called \"inconsistent\".\r\n" );
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document.write( "Edwin
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