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 inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you represent the inequality x < -1 on a graph?

Back

You draw a vertical dashed line at x = -1 and shade the region to the left of the line.

Front

What does a dashed line indicate in the graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

Front

What does a solid line indicate in the graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

Front

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

Back

Substitute the coordinates 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 > 2x - 4?

Back

You draw a dashed line for y = 2x - 4 and shade the region above the line.

Front

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

Back

The solution set is typically a shaded region on the graph where all inequalities overlap.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the solution region from the non-solution region and indicates whether points on the line are included or excluded.

Front

How can you tell if a point (0, -1) is a solution to the system y < 2 and y > 2x - 4?

Back

Substituting (0, -1) into the inequalities: -1 < 2 (TRUE) and -1 > 2(0) - 4 (FALSE). Therefore, (0, -1) is not a solution.

Front

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

Back

'y < 2x + 3' has a dashed line and does not include points on the line, while 'y ≤ 2x + 3' has a solid line and includes points on the line.