Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. Solutions are the points that satisfy all inequalities in the system.

Front

What does the symbol '>' mean in inequalities?

Back

It means 'greater than'. For example, y > 2 means y is any number greater than 2.

Front

What does the symbol '<' mean in inequalities?

Back

It means 'less than'. For example, y < 3 means y is any number less than 3.

Front

What does the symbol '≥' mean in inequalities?

Back

It means 'greater than or equal to'. For example, y ≥ 4 means y is any number greater than or equal to 4.

Front

What does the symbol '≤' mean in inequalities?

Back

It means 'less than or equal to'. For example, y ≤ 5 means y is any number less than or equal to 5.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid for ≥ or ≤, dashed for > or <). 2. Shade the region that satisfies the inequality.

Front

What is the solution set of a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system, represented by the shaded region on a graph.

Front

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

Back

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

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

What is an example of a system of inequalities?

Back

y > 2x - 4 and y < 2.