Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They can be represented using symbols such as '>', '<', '≥', and '≤'. Understanding how to manipulate and graph inequalities is crucial for solving systems of inequalities, as it allows us to determine the regions of the coordinate plane that satisfy the given conditions.
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Graphing Linear Inequalities
Graphing linear inequalities involves plotting the boundary line represented by the equation and then shading the appropriate region that satisfies the inequality. The boundary line is dashed if the inequality is strict ('>' or '<') and solid if it is inclusive ('≥' or '≤'). This visual representation helps in identifying the solution set for the system of inequalities.
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Systems of Inequalities
A system of inequalities consists of two or more inequalities that are considered simultaneously. The solution to the system is the region where the shaded areas of all inequalities overlap. Analyzing systems of inequalities is essential for determining feasible solutions in various applications, such as optimization problems in economics and engineering.
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