Systems of Linear Inequalities

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What is a system of linear inequalities?

Back

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

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What does the symbol '≤' mean in an inequality?

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The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

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

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The symbol '>' means 'greater than'. It indicates that the value on the left is strictly greater than the value on the right.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line. Then, shade the region that represents the solution set based on the inequality sign.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

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What does it mean if a point is 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 shaded region of the graph.

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How can you determine if a point is a solution to an inequality?

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To determine if a point is a solution to an inequality, substitute the coordinates of the point into the inequality and check if the statement is true.

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What is the solution set of a system of linear inequalities?

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The solution set is the region on the graph where the shaded areas of all inequalities overlap, representing all possible solutions.

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

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A system of inequalities is inconsistent if there is no solution that satisfies all inequalities, often represented by parallel lines that never intersect.

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What is the significance of the boundary line in a linear inequality?

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The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.