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 points that satisfy all inequalities in the system.

Front

How do you determine if a point is part of the solution set for a system of inequalities?

Back

To determine if a point is part of the solution set, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What does a solid line represent in graphing inequalities?

Back

A solid line represents that the points on the line are included in the solution set, indicating that the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, representing inequalities that are 'greater than' (>) or 'less than' (<).

Front

How do you graph the inequality y < 2x + 3?

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade below the line to represent all points where y is less than 2x + 3.

Front

What is the solution to the inequality a - 6 ≤ 15 + 8a?

Back

a ≥ -3.

Front

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

Back

The first step is to isolate one variable in one of the inequalities, if possible.

Front

What does it mean for a system of inequalities to be consistent?

Back

A consistent system of inequalities has at least one solution, meaning the graphs of the inequalities intersect at some point.

Front

What is the graphical representation of the solution set for a system of inequalities?

Back

The graphical representation is the shaded region where all inequalities overlap on the coordinate plane.

Front

How can you check your solution for a system of inequalities?

Back

Substitute the solution point back into each inequality to verify that it satisfies all conditions.