A2A 2.3 Systems Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

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What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, which are the points that satisfy the inequality.

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality uses < or >, meaning the boundary line is not included. A non-strict inequality uses ≤ or ≥, meaning the boundary line is included.

Front

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

Back

The boundary line divides the coordinate plane into two regions: one that contains the solutions to the inequality and one that does not.

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How do you graph a linear inequality?

Back

1. Graph the boundary line (dashed for strict, solid for non-strict). 2. Choose a test point not on the line to determine which side of the line to shade.

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

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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 a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered simultaneously.

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How can you find the feasible region for a system of inequalities?

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The feasible region is found by graphing all inequalities in the system and identifying the area where all shaded regions overlap.

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What is the role of test points in solving systems of inequalities?

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Test points help determine which regions of the graph satisfy the inequalities, allowing for the identification of the feasible region.