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

Lesson overview

Expand to review the lesson summary and core properties.

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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