Solving Systems of Linear Inequalities

The video tutorial covers solving systems of linear inequalities by first isolating variables, graphing the inequalities, and identifying solution areas through shading. It explains the use of solid and dashed lines based on inequality types and demonstrates these concepts with two examples, highlighting the importance of color-coding or labeling for clarity.

What type of line is used to graph an inequality that includes an 'equal to' component?

• Solid line

• No line

• Dashed line

• Dotted line

If an inequality has a 'greater than' symbol, where should the shading be applied on the graph?

• No shading needed

• On the line

• Above the line

• Below the line

What does the y-intercept of the equation 'y = 6x + 7' represent on a graph?

• The slope of the line

• The width of the line

• The point where the line crosses the y-axis

• The point where the line crosses the x-axis

In the context of graphing inequalities, what does a dashed line indicate?

• The inequality cannot be graphed

• The inequality is only valid at one point

• The inequality does not include an equal to

• The inequality includes an equal to

What is the slope of the line represented by the equation 'y = -1/2x - 6'?

• -1/2

• 1/2

• -2

• 2

Where do the solution regions of a system of inequalities typically appear?

• Where the lines intersect

• Where the shading does not overlap

• Where the shading overlaps

• Outside the shaded regions

If an inequality is 'greater than', where is the shading applied relative to the line?

• Above the line

• Below the line

• Directly on the line

• No shading is applied

When dividing by a negative number while solving an inequality, what must you do to the inequality sign?

• Remove the sign

• Flip the sign

• Double the sign

• Keep the sign the same

How is a vertical line graphed in the context of inequalities?

• It cannot be graphed

• Parallel to the x-axis

• Parallel to the y-axis

• Diagonally across the graph

What does a y-intercept of 4 indicate in an inequality graph?

• The line crosses the x-axis at 4

• The line is less steep than usual

• The line crosses the y-axis at 4

• The line is steeper than usual