Graphing Systems of Linear Inequalities

This lesson teaches how to graph systems of linear inequalities by shading their intersection on a coordinate plane. It explains the difference between graphing linear equations and inequalities, emphasizing the use of dotted or solid lines based on the inequality type. The lesson provides examples to illustrate how to find the intersection of solutions that satisfy both inequalities, using color shading to differentiate regions. The video concludes with a recap of the steps to graph systems of inequalities and identify the intersection of corresponding half planes.

What is the main difference between graphing systems of linear equations and linear inequalities?

• Linear inequalities use shading to show solutions.

• Linear equations require more values for x.

• Linear inequalities can have no solutions.

• Linear equations use only solid lines.

When graphing a strict inequality, what type of line should be used?

• Thick line

• Dashed line

• Double line

• Solid line

What color is used to shade the intersection of solutions in the example provided?

• Blue

• Green

• Yellow

• Red

In the example, which point is used to verify the solution for the system of inequalities?

• (3, 5)

• (-5, 3)

• (5, -1)

• (0, 0)

What does the region shaded only in blue represent in the second example?

• No solutions

• Solutions for both inequalities

• Solutions for y ≤ -2x

• Solutions for y > x + 2

What is the significance of the region that is not shaded at all?

• It satisfies neither inequality.

• It satisfies only one inequality.

• It satisfies both inequalities.

• It is irrelevant to the solution.

What is the final step in graphing systems of inequalities to find all possible solutions?

• Shade the entire graph.

• Draw solid lines for all inequalities.

• Use only dotted lines.

• Shade the intersection of half planes.