Systems of Linear Inequalities Review

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 '<' represent?

Back

The symbol '<' means 'less than' and indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '>' represent?

Back

The symbol '>' means 'greater than' and indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left is either smaller than or equal to the value on the right.

Front

What does the symbol '≥' represent?

Back

The symbol '≥' means 'greater than or equal to' and indicates that the value on the left is either larger than or equal to the value on the right.

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 point's coordinates into each inequality. If the point 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 points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

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. The line itself is included if the inequality is ≤ or ≥.

Front

How can you tell if a point is above or below a boundary line?

Back

To determine if a point is above or below a boundary line, substitute the point's coordinates into the inequality. If the inequality holds true, the point is in the corresponding region.