System of Inequality 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 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. Use a dashed line for 'greater than' or 'less than' and a solid line for 'greater than or equal to' or 'less than or equal to'. Then, shade the appropriate region for each inequality.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that a value can be either greater than or equal to a specified number.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'. It indicates that a value can be either less than or equal to a specified number.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality sign, similar to solving an equation. Remember to reverse the inequality sign if you multiply or divide by a negative number.

Front

What is the solution set of the inequality 2x - 3 < 5?

Back

The solution set is x < 4.

Front

What is the graphical representation of the inequality y > 2x + 1?

Back

The graph will have a dashed line for y = 2x + 1, and the region above the line will be shaded.

Front

What does it mean if a point lies in the solution region of a system of inequalities?

Back

If a point lies in the solution region, 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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of solutions that satisfy both inequalities simultaneously.