Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you represent inequalities graphically?

Back

Inequalities are represented on a graph by shading the region that satisfies the inequality. The boundary line can be solid (for ≤ or ≥) or dotted (for < or >).

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value can be either less than or exactly equal to a certain number.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value can be either greater than or exactly equal to a certain number.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. It indicates that one value is smaller than another.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. It indicates that one value is larger than another.

Front

When graphing the inequality y > 2, what type of line is used?

Back

A dotted line is used when graphing the inequality y > 2, indicating that points on the line are not included in the solution.

Front

What is the solution to the inequality 3x + 2 < 11?

Back

The solution is x < 3.

Front

How do you find the feasible region in a system of inequalities?

Back

The feasible region is found by graphing all inequalities and identifying the area where the shaded regions overlap.

Front

What is an example of a point that is a solution to the system of inequalities x + y ≤ 5 and x ≥ 0, y ≥ 0?

Back

(2, 3) is a solution because it satisfies both inequalities.