Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≥' mean in inequalities?

Back

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

Front

What does the symbol '≤' mean in inequalities?

Back

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

Front

How can you represent a real-world situation as a system of inequalities?

Back

Identify the constraints and objectives in the situation, then translate them into inequalities. For example, time limits, cost limits, and minimum requirements can all be expressed as inequalities.

Front

What is the feasible region in a system of inequalities?

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap. It represents all possible solutions that satisfy all inequalities.

Front

What is the significance of the boundary line in inequalities?

Back

The boundary line represents the values that make the inequality an equation. Depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥), the line may or may not be included in the solution.

Front

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