Systems of Inequalities Practice

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 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 does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if there are no points that satisfy all inequalities simultaneously, often resulting in parallel lines that never intersect.

Front

What does it mean if a system of inequalities has an infinite number of solutions?

Back

A system of inequalities has an infinite number of solutions if the inequalities overlap in such a way that there are countless points that satisfy all inequalities.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region.

Front

What is the difference between a solid line and a dashed line in graphing 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 the solution set of a system of inequalities represent?

Back

The solution set represents all the points (x, y) that satisfy all inequalities in the system, shown as the overlapping shaded regions on the graph.

Front

How can you solve a system of inequalities by graphing?

Back

To solve by graphing, graph each inequality on the same coordinate plane, identify the overlapping shaded region, which represents the solution set.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, forming the solution set.