Graphing Systems of Linear Inequalities

The video tutorial explains how to graph systems of linear inequalities in two variables. It begins with an introduction to the concept, followed by a step-by-step guide on graphing a single inequality. The tutorial then progresses to graphing multiple inequalities and finding the solution area that satisfies all conditions. An example of a more complex system of inequalities is provided, demonstrating how to graph and identify the solution region. The video emphasizes the importance of shading correctly to find the area that meets all inequality conditions.

What are we looking for when graphing systems of linear inequalities?

• The point where two lines intersect

• The area that satisfies all inequalities

• The y-intercept of the lines

• The slope of the lines

How do you graph the inequality X ≤ -2?

• Draw a vertical line at X = -2 and shade to the right

• Draw a vertical line at X = -2 and shade to the left

• Draw a horizontal line at X = -2 and shade below

• Draw a horizontal line at X = -2 and shade above

What type of line is used to graph X ≤ -2?

• Dotted line

• Curved line

• Solid line

• Dashed line

When graphing Y < -1, which direction should you shade?

• Above the line

• To the left of the line

• Below the line

• To the right of the line

What is the solution region for the inequalities X ≤ -2 and Y < -1?

• The area to the left of X = -2 and below Y = -1

• The area above both lines

• The area below both lines

• The area to the right of both lines

How do you start graphing the inequality X + Y > 5?

• By finding the x-intercept

• By finding the y-intercept and slope

• By plotting random points

• By drawing a vertical line

What kind of line is used to graph X + Y > 5?

• Dotted line

• Curved line

• Dashed line

• Solid line

When graphing 2X - Y ≤ 4, what must you remember to do after dividing by a negative?

• Subtract 1 from both sides

• Change the inequality direction

• Keep the inequality direction the same

• Add 1 to both sides

What is the solution region for the inequalities X + Y > 5 and 2X - Y ≤ 4?

• The area to the left of both lines

• The area between the two lines

• The area above both lines

• The area below both lines

How can you verify if a point lies within the solution region of both inequalities?

• By substituting the point into both inequalities

• By checking if it lies on the boundary lines

• By plotting the point on the graph

• By checking if it satisfies only one inequality