Systems/Linear Inequalities

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What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

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Shade below the line because the inequality includes 'less than'.

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What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

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What is the general form of a system of inequalities?

Back

A system of inequalities consists of two or more inequalities that share the same variables and are solved simultaneously.

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How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Use a test point to determine which side of the line to shade.

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What does it mean if a point is a solution to a system of inequalities?

Back

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

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What is the significance of the coefficients in a linear inequality?

Back

Coefficients determine the slope of the line and how steeply it rises or falls. They affect the direction of the inequality.

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How do you write a system of inequalities for a real-world problem?

Back

Identify constraints and relationships in the problem, then express them as inequalities using variables to represent quantities.

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It represents a constraint on the total number of tickets sold, where x is the number of adult tickets and y is the number of children's tickets.