Systems of Inequalities 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 graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 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.

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

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

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph will have a dashed line for y = 2x + 3, and the area below the line will be shaded.

Front

What does the solution set of a system of inequalities represent?

Back

The solution set represents all the points that satisfy all inequalities in the system, often visualized as a shaded region on a graph.

Front

What is the significance of the intersection of two shaded regions in a graph of inequalities?

Back

The intersection represents the set of solutions that satisfy both inequalities simultaneously.

Front

How do you identify the correct graph for a given inequality?

Back

Analyze the inequality to determine the boundary line (solid or dashed) and the direction of shading based on the inequality sign.

Front

What is the solution to the system of inequalities: y > x + 1 and y < -x + 4?

Back

The solution is the region where the area above the line y = x + 1 and below the line y = -x + 4 intersect.