System of Linear Inequalities

Front

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 ordered pairs 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?

Back

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 a solution.

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What does it mean if a line is solid in a graph of inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does it mean if a line is dashed in a graph of inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

Front

What is the graphical representation of a system of linear inequalities?

Back

The graphical representation consists of the shaded regions that satisfy each inequality, and the intersection of these regions represents the solution set.

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How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid or dashed line. 2. Choose a test point not on the line to determine which side of the line to shade.

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

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The intersection of shaded regions represents the set of all solutions that satisfy all inequalities in the system.

Front

What is an ordered pair in the context of linear inequalities?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on the Cartesian plane, where 'x' is the horizontal coordinate and 'y' is the vertical coordinate.

Front

How can you check if an ordered pair is a solution to a system of inequalities?

Back

Substitute the x and y values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it lies in the shaded region of the graph representing the system of inequalities.