Solving 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 inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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 symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

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

Back

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

Front

How can you determine if an ordered pair is a solution to a system of inequalities?

Back

To determine if an ordered pair is a solution, substitute the values into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

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

Back

The solution set is the set of all ordered pairs that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Front

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

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is ≤ or ≥, but not if the inequality is < or >.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution.

Front

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

Back

A feasible region is the area on a graph that satisfies all constraints of a system of linear inequalities.