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 involve 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 linear 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 a solution.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to that inequality, typically shown as a shaded region on one side of the boundary line.

Front

What is the difference between a solid line and a dashed line in the graph of linear inequalities?

Back

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

Front

What does the inequality y ≤ 2x - 1 represent graphically?

Back

It represents the region below and including the line y = 2x - 1.

Front

How can you identify the feasible region in a system of linear inequalities?

Back

The feasible region is the area where the shaded regions of all inequalities overlap. It contains all possible solutions to the system.

Front

What is the significance of the vertices of the feasible region?

Back

The vertices of the feasible region are potential solutions to the system of inequalities and are often used in optimization problems.

Front

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

Back

Graph the line y = 2x - 4 as a dashed line and shade the region above the line.

Front

What does the solution (1, 0) indicate in the context of a system of linear inequalities?

Back

The point (1, 0) is a solution, meaning it satisfies all inequalities in the system.

Front

What is the role of test points in solving systems of linear inequalities?

Back

Test points are used to determine which side of the boundary line to shade when graphing the inequalities.