Solving Systems of Inequalities By Graphing Eric Hoffman Algebra II PLHS Oct. 2007

Important Skills Work the following problems as the first part of your notes. You will be graded on this. Graph the following inequalities: x + y ≤ 3 5y – 4x < -20 Determine whether the given point satisfies each inequality: 3x + 2y ≤ 10, (2,-1) 4x – 2y > 6, (3,3)

Key Topics System of Inequalities: two or more inequalities with the same variables Solving a System of Inequalities: to solve a system of inequalities you need to find the ordered pairs that satisfy all the inequalities in the system What exactly does this mean?? Lets look at this in a graphical perspective.

Key Topics Graph the two inequalities: y < 2 – x y > x + 4 Remember: to graph inequalities, graph the boundary line and shade The region where these two inequalities “overlap” is the region that contains all the solutions to the system of inequalities

Key Topics Graph the following systems of inequalities to find the region which contains all the possible solutions: y x + 4 x – 3y > 2 and 2x – y < 4 and 2x + 4y ≥ -7

Key Topics Finding the vertices of the polygonal region formed by a system of inequalities: Find where the inequalities intersect.

Key Topics Couple of different ways to find where the inequalities intersect. Graphically Algebraically

Key Topics Homework: pg – 32 even 11 problems