System 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 'greater than' or 'less than' and a solid line for 'greater than or equal to' or 'less than or equal to'. Then, shade the appropriate region for each inequality.

Front

What does the solution to a system of inequalities represent?

Back

The solution to a system of inequalities represents all the points that satisfy all the inequalities in the system, often forming a shaded region on a graph.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means that the value is not included in the solution, while 'greater than or equal to' (≥) includes the boundary value.

Front

What does the symbol '<' represent?

Back

'<' represents 'less than', indicating that the value on the left is smaller than the value on the right.

Front

What does the symbol '≥' represent?

Back

'≥' represents 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

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

Back

To determine if a point is a solution, 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 boundary line in a system of inequalities?

Back

The boundary line represents the points where the inequalities change from true to false. It helps to define the regions that are solutions.

Front

What does it mean if a point lies on a dashed line in a graph of inequalities?

Back

If a point lies on a dashed line, it means that the point is not included in the solution set for inequalities that use 'greater than' or 'less than'.

Front

What does it mean if a point lies on a solid line in a graph of inequalities?

Back

If a point lies on a solid line, it means that the point is included in the solution set for inequalities that use 'greater than or equal to' or 'less than or equal to'.