Graphing Systems of Inequalities

The video tutorial explains how to graph a system of inequalities by finding the solution set where two inequalities overlap. It covers graphing each inequality separately using dotted lines to indicate non-inclusive boundaries and then identifies the overlapping region that satisfies both inequalities. The tutorial concludes with verifying the solution set by testing points within the overlap.

What is the main goal when graphing a system of inequalities?

• To find the union of the solution sets

• To graph each inequality separately

• To find the intersection of the solution sets

• To find the midpoint of the solution sets

What type of line is used to graph y = x - 8 when considering y > x - 8?

• Vertical line

• Dashed line

• Curved line

• Solid line

Where is the y-intercept for the line y = x - 8?

• 8

• -8

• 0

• 1

What does the slope of 1 indicate for the line y = x - 8?

• For every unit increase in y, x increases by 1

• For every unit increase in y, x decreases by 1

• For every unit increase in x, y decreases by 1

• For every unit increase in x, y increases by 1

How is the inequality y < 5 - x represented on the graph?

• With a solid line

• With a dashed line

• With a curved line

• With a vertical line

What is the y-intercept for the line y = -x + 5?

• 1

• 5

• -5

• 0

What does the slope of -1 indicate for the line y = -x + 5?

• For every unit increase in y, x decreases by 1

• For every unit increase in y, x increases by 1

• For every unit increase in x, y decreases by 1

• For every unit increase in x, y increases by 1

What is the solution set for the system of inequalities?

• The area above both lines

• The area below both lines

• The area where the two lines intersect

• The area where the two shaded regions overlap

Which point is used to verify the solution set in the video?

• (2, 2)

• (0, 0)

• (1, 1)

• (-1, -1)

Why is the point (0, 0) part of the solution set?

• Because it lies on the line y = x - 8

• Because it satisfies y > x - 8 but not y < 5 - x

• Because it satisfies y < 5 - x but not y > x - 8

• Because it satisfies both y > x - 8 and y < 5 - x