System of Inequalities Part 2

Front

What is a system of inequalities?

Back

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

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system when substituted into them.

Front

How do you determine if a point is a solution?

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality (e.g., y < mx + b).

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality (e.g., y ≤ mx + b).

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all points that satisfy the inequality, often represented graphically as a shaded region on a graph.

Front

How do you graph the inequality y < 2x + 3?

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade the area below the line to represent all points where y is less than 2x + 3.

Front

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

Back

If a point lies on the boundary line of an inequality, it is part of the solution set if the line is solid; if the line is dashed, it is not part of the solution set.

Front

Can a point be a solution to one inequality but not another in a system?

Back

Yes, a point can satisfy one inequality but not another, which means it would not be a solution to the entire system.

Front

What is the difference between '≥' and '>' in inequalities?

Back

'≥' means 'greater than or equal to' and includes the boundary line, while '>' means 'greater than' and does not include the boundary line.