System of Inequalities Graphing

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What is a system of inequalities?

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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 graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution set is where the shaded regions overlap.

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What does it mean for a point to be a solution to a system of inequalities?

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

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What is the difference between a solution and a non-solution in a system of inequalities?

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A solution is a point that satisfies all inequalities, while a non-solution does not satisfy at least one inequality.

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What does it mean if a system of inequalities has no solution?

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A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

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What does it mean if a system of inequalities has infinitely many solutions?

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A system of inequalities has infinitely many solutions if the shaded regions overlap in a way that includes an entire area or line, rather than just isolated points.

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

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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 is the significance of the boundary line in graphing inequalities?

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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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What does the symbol '>' indicate in an inequality?

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The symbol '>' indicates that the value on the left is greater than the value on the right, meaning the points above the line are included in the solution.

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What does the symbol '<=' indicate in an inequality?

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The symbol '<=' indicates that the value on the left is less than or equal to the value on the right, meaning the points on and below the line are included in the solution.