Retake 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.

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How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the appropriate region for each inequality. The solution is where the shaded regions overlap.

Front

What does 'y > mx + b' represent?

Back

It represents a linear inequality where the region above the line y = mx + b is included in the solution set.

Front

What does 'y ≤ mx + b' represent?

Back

It represents a linear inequality where the region below the line y = mx + b, including the line itself, is included in the solution set.

Front

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

Back

The boundary line separates the solution region from the non-solution region. If the inequality is strict (>, <), the line is dashed; if it includes equality (≥, ≤), the line is solid.

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 is the solution set of a system of inequalities?

Back

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

Front

What does it mean if two inequalities overlap in a graph?

Back

If two inequalities overlap, it means that there are points that satisfy both inequalities, which are part of the solution set.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' means the region below the line does not include the line itself, while 'y ≤ mx + b' includes the line in the solution set.

Front

How can you identify the feasible region in a system of inequalities?

Back

The feasible region is identified by the area where the shaded regions of all inequalities overlap on the graph.