Exploring Systems of Linear Inequalities

In this video, students learn to solve systems of linear inequalities with two variables. The tutorial covers graphing single inequalities, using slope-intercept form, and determining solution sets. Two examples illustrate the process of graphing inequalities and shading solution regions. The video concludes with graphing systems of inequalities and identifying overlapping solution areas.

What is the purpose of graphing linear inequalities?

• To solve quadratic equations

• To determine the y-intercept

• To visualize all ordered pairs that satisfy the inequality

• To find the slope of the line

What form should an inequality be in before graphing?

• Standard form

• Point-slope form

• Slope-intercept form

• Quadratic form

What should you do if you multiply or divide by a negative number when solving an inequality?

• Flip the inequality sign

• Subtract the negative number from both sides

• Keep the inequality sign the same

• Add the negative number to both sides

What type of line is used to graph an inequality that is strictly less than or greater than?

• Solid line

• Dashed line

• Bold line

• Dotted line

In Example 1, what is the slope of the line?

• 2

• 2/3

• 3/2

• 1/2

In Example 1, where do you start plotting the points?

• At the origin

• At the x-intercept

• At any random point

• At the y-intercept

In Example 2, what is the y-intercept of the line?

• 1

• 0

• 4

• 2

In Example 2, what type of line is used to graph the inequality?

• Solid line

• Dotted line

• Dashed line

• Bold line

When graphing systems of linear inequalities, what indicates the solution region?

• The area above the first line

• The overlapping shaded region

• The area below the second line

• The area outside both lines

What is the key idea when graphing systems of linear inequalities?

• To find the intersection points

• To graph each inequality separately

• To identify the region that satisfies all inequalities

• To shade the entire coordinate plane