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 a linear inequality?

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 a linear inequality?

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

Back

The graph will have a dashed line for y = 2x + 3, and the area below the line will be shaded to represent the solution set.

Front

What does the inequality 5 ≥ x represent graphically?

Back

It represents all points to the left of the vertical line x = 5, including the line itself, since it is a solid line.

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.

Front

What is the solution set of the system y ≤ 3x and y ≤ -2x + 4?

Back

The solution set is the area where both inequalities overlap, including the boundary lines.

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right, and the points on the line are not included in the solution.

Front

What is the difference between 'y < 3x' and 'y ≤ 3x'?

Back

'y < 3x' means the line is dashed and does not include points on the line, while 'y ≤ 3x' means the line is solid and includes points on the line.