Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you determine if a point is a solution to a system of linear 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 does a solid line represent in a graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in a graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

Front

What is the graphical representation of the solution set for a system of linear inequalities?

Back

The solution set is represented by the overlapping shaded regions of the inequalities on the graph.

Front

How can you identify if a point is not a solution to a system of linear inequalities?

Back

A point is not a solution if it does not satisfy at least one of the inequalities in the system when substituted into them.

Front

What is the significance of the intersection of two inequalities in a system?

Back

The intersection of two inequalities represents the common solution set that satisfies both inequalities.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a line (solid or dashed), then shade the region that satisfies the inequality.

Front

What is the difference between 'y > mx + b' and 'y ≥ mx + b'?

Back

'y > mx + b' represents a region above a dashed line, while 'y ≥ mx + b' represents a region above a solid line, including the line itself.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the line is solid (≥ or ≤) and not included if the line is dashed (> or <).