Graphing Systems of Linear Inequalities

The video tutorial explains how to solve a system of linear inequalities by graphing. It covers the process of graphing each inequality, determining the boundary lines, and shading the appropriate regions. The solution is found in the double-shaded region where both inequalities are satisfied. The tutorial provides a step-by-step guide to plotting the lines using slope-intercept form and shading the correct areas based on the inequality symbols.

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

• Check for parallel lines

• Solve for x and y

• Find the intersection point

• Graph and shade the first inequality

How do you determine the boundary line for an inequality with a 'greater than' symbol?

• Dotted line

• Thick line

• Dashed line

• Solid line

What is the slope of the first linear inequality?

• 6

• -6

• 2

• -2

Where do you plot the y-intercept for the first inequality?

• At y = -6

• At y = 0

• At y = 2

• At y = -2

What is the purpose of using a test point in graphing inequalities?

• To check for parallel lines

• To find the slope

• To determine which side to shade

• To find the y-intercept

Which point is commonly used as a test point?

• (1,1)

• (0,0)

• (-1,-1)

• (2,2)

What type of boundary line is used for an inequality with a 'less than or equal to' symbol?

• Thick line

• Dotted line

• Solid line

• Dashed line

What is the slope of the second linear inequality?

• -2/3

• 3/2

• 2/3

• -3/2

Where do you plot the y-intercept for the second inequality?

• At y = -6

• At y = 2

• At y = 0

• At y = -2

What does the double-shaded region represent in the graph of a system of linear inequalities?

• The region that satisfies only one inequality

• The region that satisfies both inequalities

• The region that satisfies the x-axis

• The region that satisfies none of the inequalities