Section 1
Equations with no solution
Property
If solving an equation with variables on both sides results in a false statement, such as or , then the equation has no solution.
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
If solving an equation with variables on both sides results in a false statement, such as or , then the equation has no solution.
Section 2
Equations with Infinitely Many Solutions
An equation has infinitely many solutions when algebraic manipulation results in a true statement where both sides are identical, such as where is any real number.
Expand to review the lesson summary and core properties.
Section 1
Equations with no solution
If solving an equation with variables on both sides results in a false statement, such as or , then the equation has no solution.
Section 2
Equations with Infinitely Many Solutions
An equation has infinitely many solutions when algebraic manipulation results in a true statement where both sides are identical, such as where is any real number.