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

What does it mean for a point to be part of the solution set of a system of inequalities?

Back

A point is part of the solution set if it satisfies all the inequalities in the system.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a 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 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' means the line is not included in the solution (dashed line), while 'y ≤ mx + b' includes the line (solid line) in the solution.

Front

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

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap, representing all possible solutions.

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 significance of the boundary line in a system of inequalities?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

What does it mean for a system of inequalities to be consistent?

Back

A system of inequalities is consistent if there is at least one solution that satisfies all inequalities.

Front

What is an example of a real-world application of systems of inequalities?

Back

A real-world application is determining the number of adult and child tickets sold at a theater to meet revenue and seating capacity constraints.

Front

How do you write a system of inequalities from a word problem?

Back

Identify the constraints and objectives in the problem, then express them as inequalities using variables to represent the quantities.