Graph the solution set of each system of inequalities. { ...

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Key Concepts

Systems of Inequalities

A system of inequalities consists of several inequalities that must be satisfied simultaneously. The solution set of the system is the common region where the individual solution sets intersect, reflecting all constraints imposed by each inequality in the system.

Intersection of Regions

The intersection of regions in the context of inequalities refers to the area on the coordinate plane where all the individual inequality conditions are met concurrently. This overlap represents the feasible solution set for the system, and identifying it requires overlaying the shaded areas of each inequality graph.

Linear Inequalities

Linear inequalities are mathematical expressions involving a linear function that use inequality symbols (such as ?, ?, <, >) instead of an equality. They describe a range of possible values for the variable rather than a single value, which is fundamental in understanding constraints and solution sets.

Graphing Linear Inequalities

Graphing linear inequalities involves drawing the boundary line represented by the corresponding linear equation and then shading the region that satisfies the inequality. Determining whether the boundary line itself is included in the solution set (solid line for ? or ?, dashed line for < or >) is an essential part of the process.

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