Solving Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities that involve 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 linear equation as a dashed or solid line, depending on whether the inequality is strict (<, >) or inclusive (≤, ≥). Then, shade the region that satisfies the inequality.

Front

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

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Front

What is the significance of the shaded area in the graph of a system of inequalities?

Back

The shaded area represents all possible solutions to the system of inequalities. Points within this area satisfy all inequalities.

Front

What does it mean if two inequalities have no overlapping shaded region?

Back

If two inequalities have no overlapping shaded region, it means that there are no solutions that satisfy both inequalities simultaneously.

Front

How do 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 difference between a solid line and a dashed line in the graph of inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

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

Back

A system of inequalities is consistent if there is at least one solution that satisfies all inequalities in the system.

Front

What is an example of a system of linear inequalities?

Back

An example is: y < 2x + 3 and y ≥ -x - 1.

Front

How can you find the solution set of a system of inequalities graphically?

Back

To find the solution set graphically, graph each inequality, shade the appropriate regions, and identify the overlapping shaded area.