2-6 Systems of Inequalities Word Problems

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

Front

How do you represent a word problem as a system of inequalities?

Back

Identify the variables, determine the constraints (inequalities), and express the conditions of the problem mathematically.

Front

What does the inequality x + y ≤ 6 represent in a word problem?

Back

It indicates that the total number of two activities (x and y) cannot exceed 6.

Front

What does the inequality 32x + 20y ≥ 150 represent in a word problem?

Back

It indicates that the total number of cookies made (32 chocolate chip cookies per hour and 20 snickerdoodle cookies per hour) must be at least 150.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients represent the rate of change or contribution of each variable to the total outcome.

Front

How do you determine the feasible region in a system of inequalities?

Back

Graph each inequality on the same coordinate plane and identify the overlapping region that satisfies all inequalities.

Front

What is the difference between a system of equations and a system of inequalities?

Back

A system of equations has exact solutions where the lines intersect, while a system of inequalities has a range of solutions represented by a region.

Front

What does it mean if a solution to a system of inequalities is on the boundary line?

Back

It means that the solution satisfies the inequality as an equality, indicating the maximum or minimum limit.

Front

How can you check if a point is a solution to a system of inequalities?

Back

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

Front

What is the graphical representation of the inequality b + t < 15?

Back

It represents all points below the line b + t = 15 in a coordinate plane.