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 involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you represent a situation with inequalities?

Back

Identify the constraints and conditions of the problem, then express them as inequalities using variables to represent unknown quantities.

Front

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

Back

It indicates that the total number of items represented by 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 difference between a system of equations and a system of inequalities?

Back

Systems of equations have specific solutions (one, none, or infinitely many), while systems of inequalities can have a range of solutions represented by a shaded region.

Front

How do you find a solution to a system of inequalities?

Back

Graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution set.

Front

What does the point (1, 0) signify in the context of a system of inequalities?

Back

It is a solution to the system, meaning it satisfies all the inequalities in the system.

Front

What is the significance of the slope-intercept form in inequalities?

Back

The slope-intercept form (y = mx + b) helps to easily graph linear inequalities by identifying the slope (m) and y-intercept (b).

Front

How do you graph the inequality x + y ≤ 6?

Back

First, graph the line x + y = 6, then shade below the line to represent all points where x + y is less than or equal to 6.

Front

What does it mean if a point lies outside the shaded region of a graph of inequalities?

Back

It means that the point does not satisfy at least one of the inequalities in the system.