Linear Inequalities and Systems of Equations

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 (>, <, ≥, ≤).

Front

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted for the variables.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a shaded region on one side of the boundary line, indicating all possible solutions.

Front

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

Back

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

Front

What is the difference between a system of equations and a system of inequalities?

Back

Systems of equations have specific solutions (one, none, or infinite), while systems of inequalities represent a range of solutions.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the specified number.

Front

What does the symbol '<' represent in a linear inequality?

Back

The symbol '<' means 'less than', indicating that the value must be strictly less than the specified number.

Front

How can you graph a linear inequality?

Back

1. Graph the boundary line as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

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

Back

The feasible region is the area on a graph where all the inequalities in a system are satisfied, representing all possible solutions.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the collection of all points that satisfy all inequalities in the system.