AA~ Solving Systems of Inequalities

Front

What does it mean to shade above or below in a graph of an inequality?

Back

Shading above indicates that the solutions are greater than the boundary line (y > mx + b), while shading below indicates that the solutions are less than the boundary line (y < mx + b).

Front

How can you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality in the system. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the inequality symbol in the context of graphing?

Back

The inequality symbol indicates whether the boundary line is included in the solution set (≥ or ≤) or not (>, <). A solid line is used for inclusive inequalities, while a dashed line is used for exclusive inequalities.

Front

How do you graph the inequality y > 2x - 4?

Back

First, graph the line y = 2x - 4 as a dashed line. Then, shade the region above the line to represent all points where y is greater than 2x - 4.

Front

What does the conjunction of two inequalities represent?

Back

The conjunction of two inequalities represents the intersection of their solution sets, meaning the solutions must satisfy both inequalities simultaneously.

Front

How do you identify the correct system of inequalities from a graph?

Back

Analyze the boundary lines and shading of the graph to determine the equations of the lines and the direction of the shading, then match them to the given systems.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (>, <) do not include the boundary line, while non-strict inequalities (≥, ≤) do include the boundary line.

Front

How do you solve a system of inequalities graphically?

Back

Graph each inequality on the same coordinate plane, then identify the region where the shaded areas overlap, which represents the solution set.

Front

What does the solution set of a system of inequalities look like?

Back

The solution set is typically represented as a shaded region on a graph, indicating all the points that satisfy all inequalities in the system.

Front

How can you check if a point lies within the solution set of a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it lies within the solution set.