solving systems of inequalities by graphing eric hoffman algebra ii plhs oct. 2007
TRANSCRIPT
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Solving Systems of Inequalities By Graphing
Eric Hoffman
Algebra II
PLHS
Oct. 2007
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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)
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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.
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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
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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
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Key Topics
Finding the vertices of the polygonal region formed by a system of inequalities:
Find where the inequalities intersect.
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Key Topics
Couple of different ways to find where the inequalities intersect.
Graphically
Algebraically
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Key Topics
• Homework: pg. 126 12 – 32 even
11 problems