Systems of Inequalities Review

Front

What is a system of inequalities?

Back

A system of 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 equation as a line. Use a solid line for inequalities that include equality (≥ or ≤) and a dashed line for strict inequalities (> or <). Then shade the region that satisfies the inequality.

Front

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

Back

'≤' 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

'≥' 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 solution set of a system of inequalities?

Back

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

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

Back

The boundary line represents the values where the inequality changes from true to false. Points on the line may be included or excluded based on whether the inequality is strict or non-strict.

Front

What does it mean if a point lies above the line in a graph of an inequality?

Back

If a point lies above the line in a graph of an inequality, it means that the point satisfies the inequality if the inequality is of the form 'y > mx + b'.

Front

What does it mean if a point lies below the line in a graph of an inequality?

Back

If a point lies below the line in a graph of an inequality, it means that the point satisfies the inequality if the inequality is of the form 'y < mx + b'.

Front

How do you write a system of inequalities from a word problem?

Back

To write a system of inequalities from a word problem, identify the variables, determine the relationships described in the problem, and express these relationships as inequalities.