Alg Systems of Inequalities Intervention

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables, representing a region on a graph where all inequalities are satisfied.

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

How do you graph the inequality y > 2x - 4?

Back

Graph the line y = 2x - 4 as a dashed line and shade above the line.

Front

What is the solution set of a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system.

Front

What does it mean if a system of inequalities has no solution?

Back

It means there is no point that satisfies all inequalities in the system.

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, it is a solution.

Front

What is the significance of the boundary line in a graph of inequalities?

Back

It separates the solution set from the non-solution set; solid lines indicate '≤' or '≥', while dashed lines indicate '<' or '>'.

Front

What does the solution (2, 2) indicate in the context of a system of inequalities?

Back

It means that the point (2, 2) satisfies all inequalities in the system.

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only.