Solving Multi-Step Equations in One Variable

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.

2x+1=20 & (I) y(2x+1) = 40 & (II)
Solve by substitution
2x+1=20 y( 20) = 40
2x+1=20 y=2

By substituting 2x+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.

Exercises
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