solving systems of inequalities by graphing eric hoffman algebra ii plhs oct. 2007
TRANSCRIPT
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 TopicsGraph the following systems of inequalities
to find the region which contains all the possible solutions:
y < 2 – x and 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. 126 12 – 32 even
11 problems