Solve the following system of linear \r\n" );
document.write( "inequalities by graphing.\r\n" );
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document.write( " 3x + 4y < 12\r\n" );
document.write( " x + 3y < 6\r\n" );
document.write( " x > 0\r\n" );
document.write( " y > 0\r\n" );
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document.write( "First get the equations of the boundary lines.\r\n" );
document.write( "These are lines whose equations are found by\r\n" );
document.write( "replace the inequality sumbols in the inequalities\r\n" );
document.write( "by equal signs. The boundary lines have these\r\n" );
document.write( "equations:\r\n" );
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document.write( " 3x + 4y = 12 has intercepts (4,0) and (0,3)\r\n" );
document.write( " x + 3y = 6 has intercepts (6,0) and (0,2)\r\n" );
document.write( " x = 0 the y-axis\r\n" );
document.write( " y = 0 the x-axis\r\n" );
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document.write( "The last two inequalities x > 0 and y > 0 restrict\r\n" );
document.write( "the graphing to the upper right hand quadrant, above\r\n" );
document.write( "the x-axis and to the right of the y-axis. Plot the\r\n" );
document.write( "intercepts and draw a DOTTED line through them. I\r\n" );
document.write( "can draw only a solid line here, but you can draw a\r\n" );
document.write( "dotted one on your paper. You would draw a solid \r\n" );
document.write( "line if the inequality symbol were \" < \" or \" >.\"\r\n" );
document.write( "But you draw a dotted line whenver the symbol is \" < \"\r\n" );
document.write( "or \" > \"\r\n" );
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document.write( "Substitute the origin (x,y) = (0,0) in each of the \r\n" );
document.write( "inequalities. If the result is a true numerical statement,\r\n" );
document.write( "then the graph of the inequality is on the side of the\r\n" );
document.write( "boundary line that the origin (0,0) is on. If the result \r\n" );
document.write( "is a false numerical statement, the graph of the \r\n" );
document.write( "inequality is on the side of the boundary line that the\r\n" );
document.write( "origin is not on. \r\n" );
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document.write( "Substituting (x,y) = (0,0) in 3x + 4y < 12\r\n" );
document.write( " 3(0) + 4(0) < 12 \r\n" );
document.write( " 0 < 12\r\n" );
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document.write( "That is true, so the graph will be on the\r\n" );
document.write( "same side of the red boundary line that the\r\n" );
document.write( "origin (0,0) is on. So it will be BELOW the\r\n" );
document.write( "red line.\r\n" );
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document.write( "Substituting (x,y) = (0,0) in x + 3y < 6\r\n" );
document.write( " (0)+ 3(0) < 6 \r\n" );
document.write( " 0 < 6\r\n" );
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document.write( "That is also true, so the graph will be on the\r\n" );
document.write( "same side of the green boundary line that the\r\n" );
document.write( "origin (0,0) is on. So it will be BELOW the\r\n" );
document.write( "green line.\r\n" );
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document.write( "So the graph is the area which is below both\r\n" );
document.write( "the red and the green line, and also which\r\n" );
document.write( "is above the x-axis and to the right of the\r\n" );
document.write( "y-axis. It is this area:\r\n" );
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document.write( "You will need to shade that area, which I can't do\r\n" );
document.write( "on here, but which you can do on your paper. You\r\n" );
document.write( "will also need to draw both the red and the green\r\n" );
document.write( "line dotted, which I also can't do here, but which\r\n" );
document.write( "you can do on your paper.\r\n" );
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document.write( "The solution is this shaded area.\r\n" );
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
