System of inequalities

Front

What is a system of inequalities?

Back

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

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.

Front

What type of line is used to represent inequalities with 'greater than' or 'less than'?

Back

A dashed line is used to represent inequalities with 'greater than' (>) or 'less than' (<) to indicate that points on the line are not included in the solution.

Front

What type of line is used to represent inequalities with 'greater than or equal to' or 'less than or equal to'?

Back

A solid line is used to represent inequalities with 'greater than or equal to' (≥) or 'less than or equal to' (≤) to indicate that points on the line are included in the solution.

Front

When graphing the inequality y < 4x + 3, which direction do you shade?

Back

You shade below the line because the inequality is 'less than'.

Front

What does it mean if a point lies above the line in a graph of an inequality?

Back

If a point lies above the line in a graph of an inequality, it means that the point does not satisfy the inequality if the inequality is 'less than'.

Front

In the context of a system of inequalities, what does the feasible region represent?

Back

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

Front

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

Back

Identify the constraints and objectives in the situation, then translate them into inequalities using variables to represent the quantities involved.

Front

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

Back

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

Front

How do you solve a system of inequalities graphically?

Back

To solve graphically, graph each inequality on the same coordinate plane, then identify the overlapping region that satisfies all inequalities.