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 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 for a point to be a solution to a system of inequalities?

Back

A point is a solution if it lies in the region where all inequalities overlap on a graph.

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 each inequality.

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. It is dashed for 'greater than' or 'less than' inequalities and solid for 'greater than or equal to' or 'less than or equal to'.

Front

How do you graph the inequality 2x - y > 4?

Back

First, graph the line 2x - y = 4 as a dashed line. Then, shade the region above the line, as the inequality indicates 'greater than'.

Front

What is the solution set of the system of inequalities 2x - y > 4 and 4x + 2y < 6?

Back

The solution set is the region where the shaded areas of both inequalities overlap on the graph.

Front

What does the term 'feasible region' refer to in the context of systems of inequalities?

Back

The feasible region is the area on the graph that satisfies all inequalities in the system, representing all possible solutions.

Front

How can you check if a point (1, 0) is a solution to the system of inequalities 2x - y > 4 and 4x + 2y < 6?

Back

Substitute (1, 0) into both inequalities: 2(1) - 0 > 4 (false) and 4(1) + 2(0) < 6 (true). Since it does not satisfy both, it is not a solution.

Front

What is the difference between 'strict' and 'non-strict' inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.