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 inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does it mean if an inequality has a solid line?

Back

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

Front

What does it mean if an inequality has a dashed line?

Back

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

Front

How do 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 graphical representation of a system of linear inequalities?

Back

The graphical representation is the shaded region on a coordinate plane where all the inequalities overlap, indicating all possible solutions.

Front

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

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Front

What does the term 'solution set' refer to in the context of linear inequalities?

Back

The solution set is the collection of all points (x, y) that satisfy all inequalities in the system.

Front

Can a system of linear inequalities have no solution?

Back

Yes, a system can have no solution if the inequalities represent parallel lines that do not intersect.

Front

What is an example of a system of linear inequalities?

Back

Example: y > 2x + 1 and y ≤ -x + 4.

Front

How can you tell if a point is above or below a line in a graph?

Back

A point is above a line if its y-coordinate is greater than the y-value of the line at the same x-coordinate; it is below if the y-coordinate is less.