Verifying Solutions to Linear Inequalities

The video tutorial covers graphing linear inequalities in two variables. It explains how ordered pairs can be solutions to these inequalities and provides two examples demonstrating the process of substituting values into inequalities to verify solutions. The first example uses the ordered pair (-3, 7) to solve the inequality 5x - 4y < -20, while the second example uses (2/3, -3/2) to solve 3x - 2y ≤ 5. The tutorial emphasizes understanding the substitution process and verifying the truth of the inequality.

What is the main topic discussed in the video?

• Graphing linear equations

• Graphing quadratic inequalities

• Solving quadratic equations

• Graphing linear inequalities in two variables

What is the significance of the inequality sign in a linear inequality?

• It determines the solution set

• It determines the direction of the graph

• It determines the y-intercept

• It determines the slope of the line

What is the significance of the inequality sign in a linear inequality?

• It determines the y-intercept

• It determines the slope of the line

• It determines the solution set

• It determines the direction of the graph

What is an ordered pair in the context of linear inequalities?

• A pair of numbers that satisfy a linear inequality

• A pair of numbers that are always greater than zero

• A pair of numbers that satisfy a linear equation

• A pair of numbers that are always equal

What does it mean if an ordered pair satisfies a linear inequality?

• The ordered pair is a solution to a linear equation

• The ordered pair is a solution to a different inequality

• The ordered pair is not a solution to the inequality

• The ordered pair is a solution to the inequality

What is the first step in solving a linear inequality?

• Graph the inequality

• Substitute values into the inequality

• Check the solution

• Simplify the expression

What is the purpose of checking if an ordered pair satisfies a linear inequality?

• To determine if the ordered pair is a solution to a linear equation

• To determine if the ordered pair is a solution to a different inequality

• To determine if the ordered pair is not a solution

• To determine if the ordered pair is a solution

What is the first step in solving a linear inequality?

• Substitute values into the inequality

• Graph the inequality

• Check the solution

• Simplify the expression

In Example 1, what inequality is being tested?

• 5x + 4y > -20

• 5x + 4y < -20

• 5x - 4y < -20

• 5x - 4y > -20

What is the first step in checking if an ordered pair is a solution to an inequality?

• Solve the inequality for y

• Solve the inequality for x

• Substitute the ordered pair into the inequality

• Graph the inequality