Equivalent Equation

Two equations are called equivalent equations if they have the same solution. Equations are often solved by applying the Properties of Equality. Each time a property is applied, an equivalent equation is produced. Consider the following equation. y + 3 = 18 To solve this equation, 3 must be subtracted from both sides.

Here, two equations that are equivalent to the given equation were created as a result of applying the Subtraction Property of Equality. They are equivalent because 15 is the solution to all these equations. I.& y+3=18 II.& y+3-3=18-3 III.& y=15 The obtained solution can be checked by substituting y=15 in the original equation. If a true statement results, the solution is correct.

A true statement was obtained. Therefore, y=15 is indeed a solution to the original equation.