System of Inequalities Review

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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 that share 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?

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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 does it mean to shade above in a graph of an inequality?

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Shading above indicates that the solutions to the inequality are all the points above the line, meaning the values of the dependent variable are greater than the values defined by the line.

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What does it mean to shade below in a graph of an inequality?

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Shading below indicates that the solutions to the inequality are all the points below the line, meaning the values of the dependent variable are less than the values defined by the line.

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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 satisfies all inequalities in the system, 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 has no solution if there is no point that satisfies all inequalities simultaneously, often due to parallel lines that never intersect.

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

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A system has infinite solutions if the inequalities represent the same line or overlapping regions, meaning any point in that region is a solution.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region based on the inequality.

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What is the significance of the inequality symbols <, >, ≤, and ≥?

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These symbols indicate the relationship between the variables: < means less than, > means greater than, ≤ means less than or equal to, and ≥ means greater than or equal to.

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Substitute the x and y values of the point into the inequality. If the resulting statement is true, the point is a solution.