Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How do you graph a linear inequality with a '>' symbol?

Back

You use a dashed line to represent the boundary, indicating that points on the line are not included in the solution.

Front

How do you graph a linear inequality with a '≥' symbol?

Back

You use a solid line to represent the boundary, indicating that points on the line are included in the solution.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

Front

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

Back

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

Front

What is the significance of the intersection of two linear inequalities?

Back

The intersection represents the set of solutions that satisfy both inequalities simultaneously.

Front

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

Back

It means that there is no point that satisfies all inequalities in the system, often due to parallel lines.

Front

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

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions.