Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities involving the same variables.

Front

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

Back

It means that the inequalities represent parallel lines that never intersect.

Front

What is the graphical representation of a linear inequality?

Back

It is represented by a shaded region on one side of a line, which can be solid or dotted.

Front

When do you use a solid line when graphing an inequality?

Back

You use a solid line for ≤ or ≥, indicating that points on the line are included in the solution.

Front

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

Back

It indicates that the values on the left are greater than the values on the right, not including the boundary.

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.

Front

What is the significance of the intersection of two lines in a system of inequalities?

Back

The intersection represents a point that satisfies both inequalities, which may be a solution.

Front

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

Back

Substitute the point's coordinates into each inequality; if all inequalities are satisfied, it is a solution.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of solutions.

Front

What does the term 'feasible region' refer to in linear programming?

Back

The feasible region is the area on a graph where all constraints of the inequalities are satisfied.