2.3 and 2.4 System of Inequalities retake

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 point's coordinates 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 when graphed.

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. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

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

Back

A feasible solution is a point that satisfies all constraints (inequalities) in the system.

Front

What is an infeasible solution in a system of inequalities?

Back

An infeasible solution is a point that does not satisfy at least one of the inequalities in the system.

Front

How can you identify a solution from a list of points?

Back

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