Solving 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 region where the graphs of the inequalities overlap.

Front

What does the symbol '≤' represent in an inequality?

Back

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

Front

What does the symbol '≥' represent in an inequality?

Back

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

Front

When graphing the inequality y < 3, what type of line is used?

Back

A dashed line is used when graphing y < 3, indicating that points on the line are not included in the solution.

Front

How do you determine the solution set for a system of inequalities?

Back

The solution set is determined by finding the region where the graphs of all inequalities overlap.

Front

What is the significance of a solid line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, used for inequalities with '≤' or '≥'.

Front

What does the inequality y > 2 represent graphically?

Back

The inequality y > 2 represents all points above the horizontal line y = 2, not including the line itself.

Front

How do you graph the inequality y ≤ 2x - 1?

Back

To graph y ≤ 2x - 1, first graph the line y = 2x - 1 with a solid line, then shade below the line.

Front

What is the first step in solving a system of inequalities by graphing?

Back

The first step is to graph each inequality on the same coordinate plane.

Front

What does the term 'feasible region' refer to in the context of systems of inequalities?

Back

The feasible region is the area on the graph where all the inequalities in the system are satisfied.