Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side of the inequality is either less than or equal to the value on the right side.

Front

How do you graph the inequality y > -4/5x - 1?

Back

To graph the inequality y > -4/5x - 1, first graph the line y = -4/5x - 1 as a dashed line (since it's a strict inequality). Then shade the region above the line.

Front

What is the significance of using a solid line when graphing inequalities?

Back

A solid line is used when graphing inequalities that include '≤' or '≥', indicating that points on the line are included in the solution set.

Front

How can 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 does the solution set of a system of inequalities represent graphically?

Back

The solution set of a system of inequalities represents the region where the shaded areas of all inequalities overlap on the graph.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., > or <) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

Front

How do you solve a system of inequalities by graphing?

Back

To solve a system of inequalities by graphing, graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the overlapping area as the solution.

Front

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

Back

The boundary line separates the solution region from the non-solution region. It is dashed for strict inequalities and solid for non-strict inequalities.