Graphing Systems of Linear Inequalities

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 (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

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

Front

What does it mean for a point to be a solution to a linear inequality?

Back

A point is a solution to a linear inequality if it lies in the shaded region of the graph, meaning it satisfies the inequality.

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 linear inequalities?

Back

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

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Front

What does it mean for a system of linear inequalities to be inconsistent?

Back

A system of linear inequalities is inconsistent if there is no point that satisfies all inequalities, meaning the shaded regions do not overlap.

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.

Front

How do you find the intersection of two linear inequalities?

Back

Graph both inequalities and identify the region where their shaded areas overlap; this region represents the intersection.

Front

What is a feasible region in the context of linear inequalities?

Back

The feasible region is the area on the graph that represents all possible solutions to the system of inequalities.