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    5.10 Systems of Linear Inequalities in Two Variables

    Figure 5.87Many college students find part-time jobs at places such as coffee shops to help pay for college.

    (credit: modification of work “TULLY’s COFFEE” by MIKI Yoshihito/Flickr, CC BY 2.0)

    Learning Objectives

    After completing this section, you should be able to:

    1. Demonstrate whether an ordered pair is a solution to a system of linear inequalities.
    2. Solve systems of linear inequalities using graphical methods.
    3. Graph systems of linear inequalities.
    4. Interpret and solve applications of linear inequalities.

    In this section, we will learn how to solve systems of linear inequalities in two variables.

    System of linear inequalities in two variables examples with answers

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  • In Systems of Linear Equations in Two Variables, we learned how to solve for systems of linear equations in two variables and found a solution that would work in both equations. We can solve systems of inequalities by graphing each inequality (as discussed in Graphing Linear Equations and Inequalities) and putting these on the same coordinate system.

    The double-shaded part will be our solution to the system. There a

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