Solving & Graphing Systems of Inequalities

Front

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 ≥.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on a coordinate plane.

Front

What is the slope-intercept form of a linear equation?

Back

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 does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the values can be equal to the boundary line or less than it.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the values can be equal to the boundary line or greater than it.

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What is the significance of a dashed line in the graph of a linear inequality?

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A dashed line indicates that the points on the line are not included in the solution set, representing strict inequalities (< or >).

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What is the significance of a solid line in the graph of a linear inequality?

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A solid line indicates that the points on the line are included in the solution set, representing inclusive inequalities (≤ or ≥).

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution set.

Front

What is the solution set of a system of inequalities?

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The solution set of a system of inequalities is the region where the shaded areas of all inequalities overlap on the graph.