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 involving the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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What does it mean if a system of linear inequalities has no solution?

Back

It means that there is no set of values for the variables that can satisfy all inequalities simultaneously, often because the lines representing the inequalities are parallel.

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What does it mean if a system of linear inequalities has an infinite number of solutions?

Back

It means that there are countless points that satisfy all inequalities in the system, typically occurring when the inequalities represent the same line or overlapping regions.

Front

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, indicating the solution set.

Front

What is the difference between a dashed line and a solid line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution (for < or >), while a solid line indicates that points on the line are included (for ≤ or ≥).

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents all points below the line y = 2x + 3, not including the line itself.

Front

How do you determine the solution set for a system of linear inequalities?

Back

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

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities simultaneously, forming the solution set for the system.

Front

What is a feasible region in the context of linear inequalities?

Back

The feasible region is the area on the graph that satisfies all inequalities in the system, often bounded by the lines of the inequalities.

Front

How can you check if a point is a solution to a system of linear inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.