Rule

Substitution Property of Equality

If two real numbers are equal, then one can be substituted for another in any expression.

If $a = b,$ then $a$ can be substituted for $b$ in any expression.

Since the Substitution Property of Equality is an axiom, it does not need a proof. This property is one of the Properties of Equality that can be used when solving equations. Consider the following example.

{2 x + 1 = 20 y (2 x + 1) = 40 (I) (II)

Solve by substitution

Substitute

$(II):$ $2 x + 1 = 20$

{2 x + 1 = 20 y (20) = 40

DivEqn

$(II):$ $LHS / 20 = RHS / 20$

{2 x + 1 = 20 y = 2

By substituting

2 x + 1

with

20

in Equation (II), the value of

y

was obtained. Note that the Substitution Property of Equality also holds true if

a

and

b

are complex numbers.

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