When we solve systems of inequalities we are looking for the intersection of its members.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
What?
We are looking for the shaded region common to all graphs. It’s the overlapping region.
This means we will be graphing systems of inequalities in order to find the solution set.
Graph of Two Linear Inequalities
First, we transform our inequalities so they are in Slope-Intercept Form.
Remember, if the inequality is either less than or greater than, then we use a dotted line when graphing. And if the inequality is either less than or equal to or greater than or equal to, we will use a solid line.
Next, we will shade the appropriate region for each inequality by choosing a point, not on the boundary and see whether its coordinate satisfies the inequality.
Finally, we determine our solution set by looking to see where the graphs overlap, as Cool Math accurately states.
You will quickly agree that solving systems of inequalities can be fun, and not too difficult.
Lastly, we will explore how to write the system of linear inequalities whose solution set is shown by the graph of the shaded region.
We will review how to write the equation of lines and Point-Slope Form, as well as verifying inequalities by testing ordered pairs.
System of Inequalities (How-To) – Video
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