24-25 - Flashcard - Graphing Systems of Eq and 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

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Front

What does the inequality y > 2x - 4 represent graphically?

Back

It represents the region above the line y = 2x - 4, not including the line itself.

Front

What does the inequality y ≤ -x - 1 represent graphically?

Back

It represents the region below the line y = -x - 1, including the line itself.

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 the point satisfies all inequalities, it is a solution.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. The type of line (dashed or solid) indicates whether points on the line are included in the solution.

Front

What is the meaning of the inequality x + y ≤ 300 in a real-world context?

Back

It means that the total number of adults (x) and children (y) in a theater cannot exceed 300.

Front

What does the inequality 7.5x + 5.5y ≥ 2000 represent in a ticket sales scenario?

Back

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

Front

How can you solve a system of inequalities graphically?

Back

By graphing each inequality on the same coordinate plane and identifying the overlapping shaded region, which represents the solution set.

Front

What is the first step in solving a word problem involving a system of inequalities?

Back

Identify the variables and write the inequalities based on the problem's constraints.