Learn on PengiPengi Math (Grade 8)Chapter 3: Solving Linear Equations

Lesson 4: Analyzing Number of Solutions (One, None, Infinite)

In this Grade 8 lesson from Pengi Math Chapter 3, students learn to classify linear equations as conditional equations, identities, or inconsistencies by analyzing coefficients and constants. By simplifying equations into the forms x = a, a = a, or a = b, students determine whether a linear equation has one solution, no solution, or infinitely many solutions. This foundational skill prepares students to interpret results like 0 = 0 or 3 = 5 and understand what each outcome means algebraically.

Section 1

Equations with no solution

Property

If solving an equation with variables on both sides results in a false statement, such as 0=100 = -10 or 3=73 = 7, then the equation has no solution.

Examples

Section 2

Equations with Infinitely Many Solutions

Property

An equation has infinitely many solutions when algebraic manipulation results in a true statement where both sides are identical, such as a=aa = a where aa is any real number.

Examples

Book overview

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Chapter 3: Solving Linear Equations

  1. Lesson 1

    Lesson 1: Simplifying and Solving One-Step & Multi-Step Equations

  2. Lesson 2

    Lesson 2: Solving Equations with Variables on Both Sides

  3. Lesson 3

    Lesson 3: Equations with Rational Coefficients (Fractions and Decimals)

  4. Lesson 4Current

    Lesson 4: Analyzing Number of Solutions (One, None, Infinite)

  5. Lesson 5

    Lesson 5: Literal Equations and Real-World Applications

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Equations with no solution

Property

If solving an equation with variables on both sides results in a false statement, such as 0=100 = -10 or 3=73 = 7, then the equation has no solution.

Examples

Section 2

Equations with Infinitely Many Solutions

Property

An equation has infinitely many solutions when algebraic manipulation results in a true statement where both sides are identical, such as a=aa = a where aa is any real number.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 3: Solving Linear Equations

  1. Lesson 1

    Lesson 1: Simplifying and Solving One-Step & Multi-Step Equations

  2. Lesson 2

    Lesson 2: Solving Equations with Variables on Both Sides

  3. Lesson 3

    Lesson 3: Equations with Rational Coefficients (Fractions and Decimals)

  4. Lesson 4Current

    Lesson 4: Analyzing Number of Solutions (One, None, Infinite)

  5. Lesson 5

    Lesson 5: Literal Equations and Real-World Applications