System of Inequalities

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 system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution set is where the shaded regions overlap.

Front

What does the solution set of a system of inequalities represent?

Back

The solution set represents all the possible values of the variables that satisfy all inequalities in the system.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

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

Back

The boundary line separates the solution set from the non-solution set. Points on one side of the line satisfy the inequality, while points on the other side do not.

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, it is included in the solution set if the inequality is ≤ or ≥, but not included if the inequality is < or >.

Front

How can you write an inequality from a word problem?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using inequality symbols based on the conditions given in the problem.

Front

What is the graphical representation of the inequality y < 2x - 4?

Back

The graph will have a dashed line for y = 2x - 4, and the area below the line will be shaded to represent all points where y is less than 2x - 4.

Front

What does the inequality y ≥ -5x - 3 represent graphically?

Back

It represents a solid line for y = -5x - 3, with the area above the line shaded, indicating all points where y is greater than or equal to -5x - 3.