## Graphing Systems of InequalitiesIf you are not familiar with graphing inequalities in DPlot, please take a look at the Graphing Inequalities page before proceeding. It includes specifics on a few DPlot operations that we'll assume you're familiar with in this topic. A "system" of inequalities is a set of inequalities, usually two or three, that you deal with all at once. The solution to the system of inequalities is simply the intersection of the solutions for each of the individual parts. The technique for solving the system is identical to that for an individual inequality, with one additional step at the end.
3x - 2y Start by transforming each inequality, when possible, into y as a function of x. Doing so gives us: y For the first two inequalities we can use the But what about the third? We cannot use - Select
*Edit Data*on the Edit menu (or click the "Edit data" button on the toolbar), select "New Curve", and enter two endpoints for a line segment with X=2. The Y values don't matter as long as the extents will cover the Y range we are interested in. The other two inequalities with X =__+__10 give us extents of roughly -25__<__Y__<__10, so the two points (2,-25) and (2,10) will work nicely. Click OK after entering those two values.
- Switch Y for X, use
*Y=f(X)*with Y=2 and -25__<__X__<__10, then swap the X and Y coordinates of this line with the*Swap X,Y*command on the Edit menu.
After setting the extents of the graph as before (using Now select the The combination of all 3 solutions is a bit busy and not especially useful: The solution we are looking for is the intersection of the three individual solutions. Return to the Note that the fill color and style from the first fill area will always be used when this option is selected; all other color and style settings are ignored. It is possible, of course, that there will be no solution to your set of inequalities. For example if you check the "Draw only the intersections of all areas" box for this graph: no fill area will be drawn, since the two areas do not overlap (and since the boundaries are parallel, they will not
overlap at We've used linear functions in the examples above for simplicity. But there is nothing restricting you from using more complex functions
(polynomials, trigonometric functions, etc.) for this technique. One important difference with non-linear inequalities is that when using
the |
RUNS ONWindows 10, Windows 8, Windows 7, 2008, Vista, XP, NT, ME, 2003, 2000, Windows 98, 95 |

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