Formative 7b

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 graph a linear inequality?

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left must be greater than 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 solution set of a system of inequalities?

Back

The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' represents a dashed line and does not include points on the line, while 'y ≤ mx + b' includes points on the line, represented by a solid line.

Front

How do you write a system of inequalities from a graph?

Back

To write a system of inequalities from a graph, identify the boundaries (lines) and determine the direction of shading (which side of the line is included) to form the inequalities.

Front

What does it mean if a solution set is unbounded?

Back

An unbounded solution set means that the solutions extend infinitely in one or more directions, often indicated by the absence of limits in the inequalities.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, forming the solution set.