SOLUTIONS TO SYSTEMS OF INEQUALITIES

Front

What is the solution set of a system of inequalities?

Back

The solution set is the common shaded region where the inequalities overlap on a graph.

Front

When is a line solid versus dotted in graphing inequalities?

Back

A solid line is used for inequalities that include equal to (≥ or ≤), while a dotted line is used for strict inequalities (< or >).

Front

What does the ordered pair (0,0) represent in a system of inequalities?

Back

(0,0) is a point that can be tested to see if it satisfies all inequalities in the system.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all inequalities, it is a solution.

Front

What does it mean if a point lies in the shaded region of a graph of inequalities?

Back

It means that the point is a solution to the system of inequalities.

Front

What is the significance of the common shaded region in graphing inequalities?

Back

The common shaded region represents all possible solutions that satisfy all inequalities in the system.

Front

How can you tell if a point is not a solution to a system of inequalities?

Back

If substituting the point into any inequality results in a false statement, it is not a solution.

Front

What is the graphical representation of the inequality y - x < 6?

Back

The line y = x + 6 is graphed as a dotted line, and the area below this line is shaded.

Front

What does the term 'inequality' mean in mathematics?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) does.