Systems of Linear Inequalities Flashcard

Front

What is a solution to a system of linear inequalities?

Back

A solution is an ordered pair (x, y) that satisfies all inequalities in the system.

Front

What does a dotted line represent in a graph of linear inequalities?

Back

A dotted line represents inequalities that are strict, such as < or >, indicating that points on the line are not included in the solution.

Front

What does a solid line represent in a graph of linear inequalities?

Back

A solid line represents inequalities that are inclusive, such as ≤ or ≥, indicating that points on the line are included in the solution.

Front

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

Back

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 graphical representation of the inequality y < 2/3x + 3?

Back

The area below the line y = 2/3x + 3 is shaded, and the line itself is dotted.

Front

What is the difference between the inequalities y ≤ 2/3x + 3 and y < 2/3x + 3?

Back

y ≤ 2/3x + 3 includes the line (solid line), while y < 2/3x + 3 does not include the line (dotted line).

Front

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

Back

The solution set is the region where the shaded areas of all inequalities overlap on the graph.

Front

What is the significance of the intersection of two linear inequalities?

Back

The intersection represents the set of points that satisfy both inequalities simultaneously.

Front

How can you graphically solve a system of linear inequalities?

Back

Graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the overlapping area.

Front

What is the role of the boundary line in linear inequalities?

Back

The boundary line divides the coordinate plane into two regions, helping to determine where the inequality holds true.