Inequalities Essay

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A "system" of linear inequalities is a set of linear inequalities that you deal with all at once. The technique for solving these systems is fairly simple. You want to make sure "y" is all by itself in your inequalities. To do so you should add or subtract all the variables and coefficients from the side "y" is on to get it alone. When solving systems you are to graph the inequalities and shade the region they share to find the solution(s). To find the solution of y>-2x+4, x>-3, y> 1 you have to graph them. To graph y>-2x+4 you start at the point (0,0) and go up on the y-axis four units and make a dot. Then you go down on the y axis two units and right one ,and continue the pattern to have a line of dots. The slope is negative two which technically is negative two over one ,and you graph the slop by doing rise over run. The line drawn to connect the dots is solid since the inequality sign is equal to. To figure out what side of the line to shade you pick any point that is not on the line. For instance if you choose the point (0,0) you will plug zero in for "x" and "y". If you do so, you end up with zero is equal to or greater than four which is not true so you should shade the side of the line that does not include that point. To graph x>-3 you start at the point (0,0) and go left three units on the x-axis. The line drawn is vertical and it is dotted because the inequality is not equal to. To know what side of the line to shade you can simply look at the inequality and know that you shade the left side of the graph because it is greater than. With greater than signs you shade the left side or the top side of the line depending on how the line is laid on the graph. To graph y>1 you start at point (0,0) and go up one unit on the y-axis. The line will be horizontal because there is no slope. The line is solid since the inequality is equal to. The shaded

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