Systems of Inequalities

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 dashed or solid line, then shade the region that satisfies the inequality (above or below the line).

Front

What does it mean if a point is 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 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 an inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point 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 to represent all points where y is less than 2x + 3.

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 the overlapping shaded regions on a graph.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection, graph both inequalities and identify the region where the shaded areas overlap; this region represents the solution to the system.

Front

What is a feasible region in the context of systems of inequalities?

Back

A feasible region is the area on a graph where all constraints (inequalities) are satisfied, representing all possible solutions.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the solution set from the non-solution set; it helps determine which side of the line satisfies the inequality.