Graphing Systems of Linear Inequalities (Part 3)

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does the solution of a system of linear inequalities represent?

Back

The solution of a system of linear inequalities represents all the points that satisfy all inequalities in the system simultaneously.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

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

Front

What does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

Front

What does it mean if a system of inequalities has infinitely many solutions?

Back

A system of inequalities has infinitely many solutions if the shaded regions overlap in such a way that there are countless points that satisfy all inequalities.

Front

What is the significance of the boundary line in a system of linear inequalities?

Back

The boundary line helps to define the regions of the graph where the inequalities hold true. It separates the solution set from the non-solution set.

Front

How do you identify the feasible region in a graph of linear inequalities?

Back

The feasible region is the area where the shaded regions of all inequalities overlap. It represents all possible solutions to the system.

Front

What is the role of the test point in graphing inequalities?

Back

A test point is a point used to determine which side of the boundary line to shade. If the test point satisfies the inequality, shade the region containing that point.