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 use symbols such as ≤ (less than or equal to) and ≥ (greater than or equal to) to indicate the range of possible solutions. Understanding how to interpret and graph inequalities is crucial for visualizing solution sets in coordinate systems.
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Graphing Systems of Inequalities
Graphing systems of inequalities involves plotting each inequality on a coordinate plane to find the region that satisfies all conditions simultaneously. The solution set is represented by the overlapping area of the graphs. This requires knowledge of how to shade regions correctly based on the inequality signs, which indicates where the solutions lie.
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Feasibility of Solutions
The feasibility of solutions refers to whether a system of inequalities has at least one solution or if it is inconsistent. A system is inconsistent if the inequalities do not overlap at any point, meaning there are no values that satisfy all inequalities simultaneously. Analyzing the graphs helps determine if a solution exists or if the system has no solution.
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Categorizing Linear Equations