Solving 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 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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How do you determine if a point is a solution to a system of linear inequalities?

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To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What does it mean to graph a linear inequality?

Back

Graphing a linear inequality involves drawing a boundary line (solid or dashed) and shading the region that represents all solutions to the inequality.

Front

When do you use a solid line when graphing inequalities?

Back

A solid line is used when the inequality includes '≤' or '≥', indicating that points on the line are included in the solution set.

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When do you use a dashed line when graphing inequalities?

Back

A dashed line is used when the inequality includes '<' or '>', indicating that points on the line are not included in the solution set.

Front

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

Back

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

Front

How can you check if a point is in the solution set of a system of inequalities?

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Substitute the point's coordinates into each inequality. If it satisfies all inequalities, it is in the solution set.

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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.

Front

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

Back

The symbol '>' indicates that the value on the left is greater than the value on the right, and points on the line are not included in the solution.

Front

What does the symbol '<' indicate in an inequality?

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The symbol '<' indicates that the value on the left is less than the value on the right, and points on the line are not included in the solution.