Systems 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

What does it mean if a line is dashed in a graph of linear inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does it mean if a line is solid in a graph of linear inequalities?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. It divides the graph into regions that represent solutions.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents the region below the line y = 2x + 3, where the line is dashed, indicating that points on the line are not included.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where all inequalities overlap, representing all possible solutions that satisfy the system.

Front

How can you graph a system of linear inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a solid line for ≤ or ≥ and a dashed line for < or >. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region.

Front

What does the inequality 5 ≥ x mean?

Back

It means that x can take any value less than or equal to 5, and the boundary line is solid because the points on the line are included.

Front

Which of the following points is NOT a solution to the system of inequalities: (0,-1), (0,3), (4,0), (6,-2)?

Back

(0,-1) is NOT a solution.