document.write( "Question 172799: Find the solution of the system of inequalities\r
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Algebra.Com's Answer #127643 by jim_thompson5910(35256)\"\" \"About 
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Graphing Inequality #1
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\n" ); document.write( "\n" ); document.write( "Inequality #1 \r
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\n" ); document.write( "\n" ); document.write( "\"2y%2Bx%3E=-2\" Start with the 1st inequality.\r
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\n" ); document.write( "\n" ); document.write( "\"2y%3E=-2-x\" Subtract \"x\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"y%3E=%28-2-x%29%2F%282%29\" Divide both sides by \"2\" to isolate \"y\".\r
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\n" ); document.write( "\n" ); document.write( "\"y%3E=-%282%29%2F%282%29-%28x%29%2F%282%29\" Break up the fraction.\r
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\n" ); document.write( "\n" ); document.write( "\"y%3E=-1-%281%2F2%29x\" Reduce\r
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\n" ); document.write( "\n" ); document.write( "\"y%3E=-%281%2F2%29x-1\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "So in order to graph \"y%3E=-%281%2F2%29x-1\", we need to graph the equation \"y=-%281%2F2%29x-1\"\r
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\n" ); document.write( "\n" ); document.write( " Graph \"y=-%281%2F2%29x-1\"\r
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\n" ); document.write( "\n" ); document.write( "Now since the inequality sign of \"y%3E=-%281%2F2%29x-1\" is a \"greater-than or equal to\" sign, this tells us to shade the region above the graph (since points in that region have larger y values)\r
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\n" ); document.write( "\n" ); document.write( "So the shading looks like this:\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y%3E=-%281%2F2%29x-1\" with the shaded region in green\r
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\n" ); document.write( "\n" ); document.write( "Inequality #2 \r
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\n" ); document.write( "\n" ); document.write( "\"y%2B2x%3C4\" Start with the 2nd inequality.\r
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\n" ); document.write( "\n" ); document.write( "\"y%3C4-2x\" Subtract \"2x\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"y%3C-2x%2B4\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "So in order to graph \"y%3C-2x%2B4\", we need to graph the equation \"y=-2x%2B4\"\r
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\n" ); document.write( "\n" ); document.write( " Graph \"y=-2x%2B4\"\r
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\n" ); document.write( "\n" ); document.write( "Now since the inequality sign of \"y%3C-2x%2B4\" is a \"less-than\" sign, this tells us to shade the region below the graph (since points in that region have smaller y values)\r
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\n" ); document.write( "\n" ); document.write( "So the shading looks like this:\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y%3C-2x%2B4\" with the shaded region in green\r
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\n" ); document.write( "\n" ); document.write( "Finally, to graph \"y%3E3\", we need to graph \"y=3\" (which is a horizontal line at y=3) like this\r
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\n" ); document.write( "\n" ); document.write( " Graph \"y=3\"\r
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\n" ); document.write( "\n" ); document.write( "Now shade the region above the line (since the sign is a \"greater-than\" sign) to get\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y%3E3\" with the shaded region in green\r
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\n" ); document.write( "\n" ); document.write( "Graphing the inequalities together on the same coordinate systems\r
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\n" ); document.write( "\n" ); document.write( "Now simply graph the inequalities together. To do this, simply graph each line together and their corresponding region to get (note: use different colors to represent the shaded regions)\r
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\n" ); document.write( "\n" ); document.write( "Here is a cleaner look at the intersection of regions\r
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\n" ); document.write( "\n" ); document.write( " Here is the intersection of the 3 regions represented by the series of dots\r
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\n" ); document.write( "\n" ); document.write( "So the solution of the system of inequalities is\r
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