Graphing Systems of Linear Inequalities

The video tutorial explains systems of inequalities, which are two or more inequalities with the same variables. It covers how to graph these systems by converting inequalities into slope-intercept form, using solid or dashed lines, and shading regions. The solution set is the overlapping shaded region. Several examples are provided, demonstrating graphing techniques and verifying solutions algebraically and graphically. The tutorial also discusses scenarios with no solutions due to parallel lines.

What is a system of inequalities?

• A single inequality with one variable

• Two or more inequalities with different variables

• Two or more inequalities with the same variables

• A graphical representation of an equation

How do you graph a system of inequalities?

• By drawing a circle around the origin

• By solving each inequality for zero

• By converting each inequality into slope-intercept form and shading appropriately

• By plotting points randomly

What does a dashed line represent in a graph of inequalities?

• None of the above

• Inequality including the line

• Inequality without including the line

• Equality

What does a solid line indicate in a graph of inequalities?

• The inequality does not include the line

• The inequality includes the line

• The line is not part of the inequality

• The line represents an equation

Is the point (0,1) a solution to the graphed system of inequalities?

• No, it lies outside the shaded regions

• Yes, but only for one inequality

• Yes, it lies in the overlapping region

• No, it does not satisfy both inequalities

What does shading below the line indicate in the context of inequalities?

• None of the above

• y is greater than the expression

• y is equal to the expression

• y is less than the expression

What happens to the inequality sign when you divide by a negative number?

• It becomes an equality

• It is reversed

• It is removed

• It remains the same

Can a system of parallel lines have a solution?

• Yes, always

• Yes, if they intersect

• Only if they are not shaded

• No, never

What is the slope of the line represented by the equation 3x - 4y > 8 after converting to slope-intercept form?

• 3/4

• 4/3

• -4/3

• -3/4

Is the point (8, -1) a solution to the final graphed system of inequalities?

• Yes, it is in the overlapping region

• No, it does not lie in the shaded area

• Yes, but only satisfies one inequality

• No, it is outside all shaded regions