Graphing Systems of Inequalities: Key Concepts and Techniques

This video tutorial guides viewers through solving systems of inequalities using graphing techniques. It covers four different systems, explaining how to graph each inequality, determine the type of line (solid or dashed), and identify the correct region to shade. The video emphasizes using test points to verify solutions and concludes with a preview of the next tutorial.

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

• Shade the region above the line

• Find the intersection points

• Use the quadratic formula

• Graph each line like y = mx + b

How do you determine the type of line to draw for an inequality?

• By using the quadratic formula

• By calculating the y-intercept

• By finding the slope

• By checking if the inequality is strict or non-strict

What is the y-intercept of the first inequality in the second system?

• 2

• -2

• -5

• 0

How do you decide which side of the line to shade?

• By using a test point

• By finding the slope

• By checking the x-intercept

• By calculating the y-intercept

What is the slope of the first inequality in the third system?

• -5

• 1/2

• -2

• 5/3

What type of line is used for the inequality y < -2x - 3?

• Dashed

• Solid

• Curved

• Vertical

What is the x-intercept of the line x = -3?

• -3

• 0

• -5

• 3

How do you plot the line for the inequality x ≤ -3?

• Draw a vertical line at x = -3

• Draw a horizontal line at y = -3

• Draw a line with slope 3

• Draw a line with slope -3

What is the slope of the line y < 5/3x + 2?

• -2

• 5/3

• -5/3

• 2

Why is it useful to use the test point (0,0) when solving inequalities?

• Because it is always in the shaded region

• Because it is the midpoint of the graph

• Because it is always on the line

• Because any number times 0 is 0, making calculations easier