Lesson 7.5

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Systems of inequalities are the next step after solving a system of equations, but we'll still be using everything eventually. In order to solve a system of inequality, a graph will be needed in order to find the solution that will satisfy all the inequalities.

 

Here are the steps:

Replace the inequality sign with a equal sign, and sketch the graph of the resulting equation.

 >dashed lines (greater than or less than) 

 >solid lines (greater than or equal to or less than or equal to)

Test one point in each regions formed by the graph in step 1. If the point satisfies the inequality, shade the entire region to denote that every point in the region satisfies the inequality.

Solution of a system of inequalities in x and y is a point (x,y) that satisfies each inequality in the system

For a system of inequalities it is helpful to find the vertices of the solution region.

Here's an example: 

Just always remember to check which vertices satisfy the inequality that includes x and y!