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

Front

What does it mean to shade below in a graph of an inequality?

Back

Shading below indicates that the solutions to the inequality are all the points below the line, including the line if the inequality is less than or equal to (≤).

Front

What is the difference between < and ≤ in inequalities?

Back

The symbol < means 'less than' and does not include the boundary line, while ≤ means 'less than or equal to' and includes the boundary line.

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 part of the solution set.

Front

What does the inequality y > 3x - 2 represent graphically?

Back

It represents the region above the line y = 3x - 2, not including the line itself.

Front

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

Back

The boundary line separates the solution set from the non-solution set. Whether the line is included in the solution depends on the inequality symbol.

Front

How do you graph the inequality y ≥ -3?

Back

Graph the horizontal line y = -3 and shade the region above the line, including the line itself.

Front

What is a solution to the system of inequalities?

Back

A solution to the system is any point that satisfies all inequalities in the system.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is ≤ or ≥.

Front

How can you tell which direction to shade when graphing an inequality?

Back

You can determine the shading direction by testing a point not on the line (usually (0,0)) in the inequality. If the inequality holds true, shade the region containing that point.