Graphing Systems of Inequalities Topic Index | Algebra Index | Regents Exam Prep Center
 If you can graph an inequality, you can graph a system of inequalities! Simply graph each inequality separately on the same set of axes.  The area where the shadings overlap is the solution to the system of inequalities.
 To Graph a System of  Inequalities 1.  Graph each inequality separately.  The directions for graphing inequalities can be found in "Graphing Inequalities". 2.  The solution to the system, will be the area where the shadings from each inequality overlap one another.
 Graph the following  system of inequalities

 Graph the system Graph each inequality as if it was stated in "y=" form.  If the inequality is < or > a dotted line must be used to represent the line.  If the inequality is < or >, a solid line is used.   Choose a test point to determine which side of the line needs to be shaded.  The test point for this problem was (0,0).  Always pick a point that is easy to work with. For the test point (0,0), 0 < 2(0)-3  False 0 (-2/3)0+2 False Since both equations were false, shading occurred on the other side of the line, not covering the point. The solution, S, is where the two shadings overlap one another.

Applied Example Using a System of Linear Inequalities
The "We Sell CDs" website plans to purchase ads in a local newspaper advertising their site.  Their operating budget will allow them to spend at most \$2200 on this advertising adventure.  They plan to run at most 20 ads.  An ad will cost \$50 to appear in the weekday paper and \$200 to appear in a weekend edition.  Prepare a graph that will represent all of the possible combinations of ads under these conditions.