Solving Systems of Inequalities Challenge

The video tutorial explains how to solve systems of linear inequalities by graphing. It covers the basics of graphing linear inequalities, including shading regions to find solution sets. The tutorial provides examples to illustrate how to graph inequalities, identify overlapping solution areas, and handle cases with parallel lines that may result in no solution.

What is a system of linear inequalities?

• A set of two or more linear equations in different variables.

• A set of two or more linear inequalities in the same variable.

• A single linear inequality.

• A set of quadratic equations.

What does the solution set of a system of linear inequalities represent?

• All the points that satisfy at least one inequality.

• A single point where the lines intersect.

• The area outside the shaded regions.

• All the points that satisfy all inequalities in the system.

How is the graph of y > x + 2 represented?

• As a solid line with shading below.

• As a dashed line with shading above.

• As a dashed line with shading below.

• As a solid line with shading above.

In the first example, what type of line is used for y ≤ 3?

• Dashed line

• Solid line

• Dotted line

• No line

In the first example, where do you shade for y > x + 2?

• Below the line

• Above the line

• On the line

• No shading

In the second example, what is the slope of the line y > 2x - 3?

• 2

• 1

• -2

• 0.5

In the second example, what type of line is used for y ≥ 1/2x + 1?

• No line

• Solid line

• Dashed line

• Dotted line

What does it mean when two lines in a system of inequalities are parallel?

• They have the same slope.

• They intersect at one point.

• They will always have a solution set.

• They have the same y-intercept.

In the third example, what is the result when the solution sets of two parallel lines do not overlap?

• No solution

• One solution

• Two solutions

• Infinite solutions

Can parallel lines in a system of inequalities sometimes have a solution set?

• No, they always have no solution.

• Yes, if they intersect at one point.

• No, they never have a solution set.

• Yes, if the shading overlaps.