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 ordered pairs that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the appropriate region (above or below the line) based on the inequality sign. The solution is where the shaded regions overlap.

Front

What does the inequality symbol '>' indicate?

Back

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

Front

What does the inequality symbol '<' indicate?

Back

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

Front

What does the inequality symbol '≥' indicate?

Back

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

Front

What does the inequality symbol '≤' indicate?

Back

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

Front

How do 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 of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What is the significance of shading in the graph of inequalities?

Back

Shading indicates the region of the graph where the solutions to the inequality are located. The direction of shading depends on the inequality sign.

Front

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

Back

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

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Shade the appropriate area for each inequality. 3. The solution is the region where the shaded areas overlap.