Solving Systems of Inequalities Graphing Lesson

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are solved together.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

It means that the point satisfies all inequalities in the system.

Front

What is the difference between '>' and '≥'?

Back

'>' means the value is greater than, while '≥' means the value is greater than or equal to.

Front

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

Back

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

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all possible solutions to the system of inequalities.

Front

What does the intersection of two shaded regions represent?

Back

It represents the set of solutions that satisfy both inequalities in the system.

Front

How do you find the boundary line for a linear inequality?

Back

Convert the inequality to an equation (replace < or > with =), then graph the line.

Front

What is the solution set of a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system.

Front

What does it mean if a solution set is empty?

Back

It means there are no points that satisfy all inequalities in the system.