Warm Up 12/6 Unit 3 Lesson 20

Front

What is a solution in the context of a system of inequalities?

Back

A solution is a set of values for the variables that satisfies all inequalities in the system.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If all inequalities are satisfied, the point is a solution.

Front

What is the significance of the inequality x + y ≤ 300 in a ticket sales scenario?

Back

It represents the maximum number of tickets (adults and children) that can be sold, given the theater's seating capacity.

Front

What does the inequality 7.5x + 5.5y ≥ 2000 represent?

Back

It indicates that the total revenue from ticket sales must be at least $2000.

Front

Is (0, 0) a solution to the system of inequalities x + y ≤ 300 and 7.5x + 5.5y ≥ 2000?

Back

No, (0, 0) is not a solution because it does not satisfy the revenue inequality.

Front

Is (-2, 4) a solution to the system of inequalities x + y ≤ 300 and 7.5x + 5.5y ≥ 2000?

Back

Yes, (-2, 4) is a solution as it satisfies both inequalities.

Front

Which of the following points is not a solution to the system: (0, -1), (0, 3), (4, 0), (6, -2)?

Back

(0, -1) is not a solution as it does not satisfy the inequalities.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

It means that the point satisfies the inequality as an equality.

Front

What is the graphical representation of a system of inequalities?

Back

It is the shaded region on a graph that shows all possible solutions that satisfy all inequalities.

Front

How can you graph the inequality x + y ≤ 300?

Back

First, graph the line x + y = 300, then shade below the line to represent all points where x + y is less than or equal to 300.