###### 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

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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

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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.