System 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 share 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 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 does a solid line represent in the graph of an 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 the graph of an 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 inequality y < 2x + 3?

Back

The graph will show a dashed line for y = 2x + 3, and the area below the line represents the solution set.

Front

What is the solution set of the system of inequalities y > x + 1 and y < -x + 4?

Back

The solution set is the region where the area above the line y = x + 1 and below the line y = -x + 4 overlap.

Front

How can you graph a system of linear inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use solid or dashed lines as appropriate. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Front

What is the significance of the point (1, 1) in the context of a system of inequalities?

Back

The point (1, 1) is a solution to the system of inequalities if it satisfies all inequalities in the system.

Front

What does it mean if a point is not a solution to a system of inequalities?

Back

If a point is not a solution, it means that when substituted into the inequalities, it does not satisfy at least one of them.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) does not include the boundary line, while 'greater than or equal to' (≥) includes the boundary line in the solution set.