5A Graphing systems of Linear Inequalities

Front

What is a linear inequality?

Back

Front

What does it mean for a system of linear inequalities to have no solution?

Back

A system of linear inequalities has no solution when the inequalities represent parallel lines that do not intersect.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a boundary line, which can be solid (inclusive) or dashed (exclusive).

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

Front

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

Back

Front

What does the term 'feasible region' refer to in the context of linear inequalities?

Back

The feasible region is the area on the graph where all the solutions to the system of inequalities exist. It is the intersection of all half-planes.

Front

How can you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, first graph each inequality as a line, then shade the appropriate half-plane for each inequality. The overlapping shaded area represents the solution set.

Front

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

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. It is crucial for determining the feasible region.

Front

What does it mean for a system of inequalities to have an infinite number of solutions?

Back

A system of inequalities has an infinite number of solutions when the feasible region is unbounded or when the inequalities overlap significantly.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the slope and y-intercept of the boundary line, and determine whether the line is solid or dashed to decide on the inequality symbol.