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

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

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it lies in the region defined by the inequalities.

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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

Front

What does the symbol '>' mean in an inequality?

Back

'>' means 'greater than'. For example, x > 2 means x can take any value greater than 2.

Front

What does the symbol '<' mean in an inequality?

Back

'<'' means 'less than'. For example, y < 4 means y can take any value less than 4.

Front

What does the symbol '≥' mean in an inequality?

Back

'≥' means 'greater than or equal to'. For example, x ≥ 3 means x can be 3 or any value greater than 3.

Front

What does the symbol '≤' mean in an inequality?

Back

'≤' means 'less than or equal to'. For example, y ≤ 5 means y can be 5 or any value less than 5.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Then shade the region that satisfies the inequality.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the intersection of the solution sets of each inequality, represented by the overlapping shaded regions on the graph.