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Inequalities (systems & graphs): FAQ

Frequently asked questions about systems and graphs of inequalities

Why do we need to learn how to check solutions of two-variable inequalities?

We need to learn this skill in order to verify whether or not a given coordinate point satisfies an inequality. Checking solutions is essential for being able to graph inequalities and model real-life situations with them.

What are some real-world applications of linear inequalities?

Linear inequalities can be used in a variety of real-world contexts. For example, they can be used to model constraints for a manufacturing company or to create a budget in personal finance. They can also be used to solve optimization problems or analyze data sets.

How do we graph two-variable inequalities?

There are a few steps to graphing two-variable inequalities. First, we graph the corresponding equation as if it were an equality. Then we use a test point to determine which side of the line we should shade in order to represent the inequality. Finally, we show whether or not the line itself is included in the solution set by drawing it as a solid or dashed line.

How do we graph a system of linear inequalities?

When graphing a system of linear inequalities, we follow the same process we do for graphing a single inequality, but we have to do it multiple times. For each inequality in the system, we graph the corresponding equation as an equality, determine which side of the line to shade, and decide whether to draw a solid or dashed line. Once we have graphed all of the inequalities, the solution set is the region where all of the shaded regions overlap.

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