Systems of Equations and Inequalities (Graphs) #1

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What does it mean for a point to be 'not a solution' in a system of inequalities?

Back

A point is 'not a solution' if it does not satisfy at least one of the inequalities in the system.

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What is the graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of each inequality.

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What is the significance of the boundary line in a system of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

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How can you identify a solution from a set of points?

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To identify a solution, check each point by substituting its coordinates into the inequalities. The point that satisfies all inequalities is the solution.

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What is the difference between a solution to an equation and a solution to an inequality?

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A solution to an equation is a specific point that makes the equation true, while a solution to an inequality is a range of values that satisfy the inequality.

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What does it mean for a point to be on the boundary line of an inequality?

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A point on the boundary line satisfies the equation of the line but may or may not satisfy the inequality, depending on whether the inequality is strict or inclusive.

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How do you graph a system of inequalities?

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To graph a system of inequalities, graph each inequality as a line, shade the appropriate region for each inequality, and identify the overlapping shaded region as the solution set.

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What is the role of test points in solving inequalities?

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Test points are used to determine which side of the boundary line satisfies the inequality. By testing a point not on the line, you can identify the solution region.