Systems of Inequalities

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 set of all points that satisfy all inequalities in the system.

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 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 graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane. The boundary line is dashed if the inequality is strict ('<' or '>') and solid if it includes equality ('≤' or '≥').

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap. It contains all points that satisfy all inequalities.

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a dashed line for strict inequalities and a solid line for inclusive inequalities. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region.

Front

What is an example of a system of inequalities?

Back

y < 2x + 3 and y ≥ -x - 1.

Front

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

Back

If a point lies on the boundary line, it is a solution if the inequality includes equality (≤ or ≥). If the inequality is strict (< or >), the point is not a solution.

Front

What is the difference between 'solution' and 'not a solution' in the context of inequalities?

Back

A 'solution' satisfies all inequalities in the system, while 'not a solution' does not satisfy at least one inequality.