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Systems of Inequalities  Concept
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
When solving systems of inequalities, you are solving for a solution region. A solution region is the collection of points that are solutions to both inequalities. Solving systems of inequalities combines knowledge of graphing lines, graphing inequalities and solving systems of equations.
Solving systems of inequalities is getting a little tricky in your Math class cause you're going to have to combine everything you know about graphing lines, graphing inequalities and systems of equations in order to do these problems.
When you're solving them you're looking for what's called a solution region. The Solution region for a system of inequalities is the collection of points that are all solutions to both inequalities. Here's what it's going to look like, remember when you're graphing inequalities that sometimes you have dashy lines and sometimes you have solid lines but you always have some shading going on. So I just made this up I'm not showing you these equations but let's just say that when I graphed my first line here that's the solid guy that I shaded above the line. Then let's say that when I graphed the second line this dashy one that I solved over here that I shaded over here. What that means is that the solution region is where my two shadings overlap. It's this [IB] area right there. You have to be really careful that I have the two boundary lines, this one in this case happen to be that solid guy and that dash guy.
What this means is that any point I picked in this darken solution region where my purplish and my blue overlapped that would be a point that works in both original inequalities. So when you're doing these graphs it's a good idea to get out your colored pencils cause you're going to end up with lots of different shading overlapping. And if just use pencils sometimes it's hard to see your solution region.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
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Sample Problems (9)
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Systems of Inequalities
Problem 1 8,076 viewsGraph:
y > 3x − 2y ≤ ½x + 4 
Systems of Inequalities
Problem 2 5,476 viewsGraph:
2y > 4x + 6y > 5 
Systems of Inequalities
Problem 3 4,403 viewsGraph:
y > ¾x − 2y < ¾x − 3 
Systems of Inequalities
Problem 4 4,933 viewsYou buy ground beef and ground turkey in bulk to make different kinds of chili at your restaurant. Ground beef costs $1.50⁄lb and ground turkey costs $2.50⁄lb. You want to spend no more than $9.50 total and you need at least 4 lbs of meat.
a) Write a system of inequalitiesb) Graph the system to show all possible solutions. 
Systems of Inequalities
Problem 5 284 views 
Systems of Inequalities
Problem 6 246 views 
Systems of Inequalities
Problem 7 276 views 
Systems of Inequalities
Problem 8 271 views 
Systems of Inequalities
Problem 9 307 views
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