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 points that satisfy all inequalities in the system.

Front

How do systems of equations differ from systems of inequalities?

Back

Systems of equations can have one solution, no solution, or infinitely many solutions, while systems of inequalities can have a range of solutions.

Front

If x is the number of 2-point shots and y is the number of 3-point shots, what inequalities represent scoring at least 20 points in less than 10 shots?

Back

x + y < 10 and 2x + 3y ≥ 20.

Front

What does the inequality x + y < 10 represent in a word problem?

Back

It represents a constraint on the total number of items (x and y) that can be chosen, indicating that the total must be less than 10.

Front

What does the inequality 2x + 3y ≥ 20 represent in a word problem?

Back

It represents a requirement that the total score from the shots (2 points for each 2-point shot and 3 points for each 3-point shot) must be at least 20 points.

Front

What is the significance of the inequality symbol < in a word problem?

Back

The symbol < indicates that the value on the left must be less than the value on the right, representing a strict upper limit.

Front

What does the inequality symbol > indicate in a word problem?

Back

The symbol > indicates that the value on the left must be greater than the value on the right, representing a strict lower limit.

Front

How can you represent the cost of coffee and doughnuts with equations based on Joe's purchases?

Back

You can use the equations 10c + 5d = 16.50 and 5c + 10d = 14.25 to represent the total costs.

Front

What does the inequality < 180 days left of school mean?

Back

It means that the number of days remaining is less than 180, indicating a countdown to the end of the school year.

Front

What does the inequality > 90 in Math mean for Haley?

Back

It means that Haley hopes to achieve a score greater than 90 in Math this quarter.