Systems of Linear Inequalities

Front

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 a dotted line represent in a graph of linear inequalities?

Back

A dotted line represents inequalities that are strict, such as < or >, indicating that points on the line are not included in the solution set.

Front

What does a solid line represent in a graph of linear inequalities?

Back

A solid line represents inequalities that are inclusive, such as ≤ or ≥, indicating that points on the line are included in the solution set.

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

Back

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

Front

What is the graphical representation of the inequality y > x - 2?

Back

The graphical representation is a region above the line y = x - 2, with a dotted line indicating that points on the line are not included.

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What is the graphical representation of the inequality y ≤ x + 3?

Back

The graphical representation is a region below or on the line y = x + 3, with a solid line indicating that points on the line are included.

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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.

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What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it may or may not be a solution, depending on whether the inequality is strict or inclusive.

Front

How can you graph a system of linear inequalities?

Back

To graph a system, first graph each inequality as a line (dotted or solid), then shade the appropriate region for each inequality, and identify the overlapping region.

Front

What is the significance of the intersection of shaded regions in a graph of linear inequalities?

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The intersection of shaded regions represents the set of all points that satisfy all inequalities in the system, which is the solution set.