Types of Solutions in Equations

In this lesson, Mr. Holcomb explains the classification of solutions for linear equations. The video covers solving equations, checking solutions, and understanding different types of solutions such as one solution, no solution, and infinite solutions. Examples are provided to illustrate each type, and viewers are guided through creating equations with specific solution types.

What is the first step in solving the equation 7x - 5 = 5x + 3?

• Add 3 to both sides

• Multiply both sides by 2

• Subtract 5x from both sides

• Add 5 to both sides

If the coefficients of x are the same on both sides of an equation, but the constants are different, what type of solution does the equation have?

• No solution

• Infinite solutions

• Two solutions

• One solution

In the equation 3x + 5 = 3x + 5, what type of solution is present?

• Infinite solutions

• No solution

• Two solutions

• One solution

What happens when the coefficients are different and the constants are the same in an equation?

• No solution

• Infinite solutions

• Two solutions

• One solution

Which of the following equations has no solution?

• 5x + 3 = 5x + 3

• 4x + 2 = 4x + 5

• 3x + 7 = 3x + 7

• 2x + 1 = 2x + 1

How can you create an equation with one unique solution?

• Same coefficients, same constants

• Different coefficients, different constants

• Different coefficients, same constants

• Same coefficients, different constants

Which equation represents infinitely many solutions?

• 6x + 4 = 6x + 4

• 5x + 3 = 5x + 2

• 4x + 1 = 4x + 5

• 3x + 7 = 3x + 8

What is the result when both coefficients and constants are the same in an equation?

• One solution

• Two solutions

• No solution

• Infinite solutions

What type of solution is present if the equation is 7x + 2 = 7x + 3?

• Two solutions

• Infinite solutions

• No solution

• One solution

Which of the following is true for an equation with different coefficients and different constants?

• It has no solution

• It has one solution

• It has two solutions

• It has infinite solutions