Understanding Systems of Inequalities

The video tutorial explains how to solve systems of inequalities by graphing. It covers the process of graphing individual inequalities, using dashed and solid lines to represent different inequality symbols, and finding intercepts to plot lines. The tutorial also demonstrates how to use test points to determine which regions satisfy the inequalities. Finally, it shows how to identify the overlapping region that represents the solution to the system of inequalities.

What is the solution to a system of inequalities?

• A dashed line on a graph

• A single ordered pair that satisfies one inequality

• A set of ordered pairs that satisfy all inequalities

• A graph of a single inequality

What does a dashed boundary line indicate in the graph of an inequality?

• The inequality has no solution

• The inequality is an equation

• The points on the line are not part of the solution

• The points on the line are part of the solution

How do you determine the y-intercept of the line 3x - 2y = 12?

• Set y to 0 and solve for x

• Set x to 0 and solve for y

• Use the midpoint formula

• Use the slope-intercept form

What is the x-intercept of the line 3x - 2y = 12?

• (0, 4)

• (4, 0)

• (-6, 0)

• (0, -6)

Which test point is commonly used to determine the solution region of an inequality?

• (1, 1)

• (-1, -1)

• (0, 0)

• (2, 2)

What does a solid boundary line indicate in the graph of an inequality?

• The inequality has no solution

• The points on the line are not part of the solution

• The inequality is an equation

• The points on the line are part of the solution

How is the compound inequality -3 ≤ y ≤ 2 represented on a graph?

• With a single solid line

• With a single dashed line

• With two solid lines

• With two dashed lines

What region represents the solution to the compound inequality -3 ≤ y ≤ 2?

• Outside y = -3 and y = 2

• Between y = -3 and y = 2

• Below y = -3

• Above y = 2

What is the solution to the system of inequalities?

• The region above both lines

• The region below both lines

• The overlapping region between the two horizontal lines and on one side of the dashed line

• The entire coordinate plane

Which points are included in the solution of the system of inequalities?

• All points on the graph

• Points on the horizontal boundary lines

• Points on the dashed line

• Points outside the shaded region