AA~ 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 graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as if it were an equality. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. Then, shade the region that satisfies the inequality.

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does it mean if a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

Front

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

Back

To determine if a point is a solution, 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 shaded regions in a graph of inequalities?

Back

The intersection of shaded regions represents the solution set of the system of inequalities, where all conditions are satisfied.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means greater than and does not include the boundary line, while '≥' means greater than or equal to and includes the boundary 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 solution set of a system of inequalities look like on a graph?

Back

The solution set is represented by the overlapping shaded regions of the inequalities on the graph.

Front

How do you identify the boundary line of an inequality?

Back

The boundary line is identified by rewriting the inequality as an equation (e.g., y = mx + b) and then graphing that line.