Which statement illustrates the substitution property?

Which statement illustrates the substitution property?

• A. Graphing functions to find intersection
• B. Substituting a value for a variable or expression into an equation
• C. Adding the same number to both sides
• D. Factorizing and setting each factor equal to zero

Answer: (B)

The substitution property of equality is the rule that you can replace a variable or expression with another expression that is equal to it in any equation or expression, and the value stays the same. This is what you use when you know a variable equals a certain number and you want to simplify or solve by plugging that number in. For example, if x equals 5, then in any equation you can substitute 5 for x. In a simple equation like 2x + 7 = 17, substituting x = 5 gives 2(5) + 7 = 17, which checks out as 17 = 17. More generally, if two expressions are equal, you can replace one with the other anywhere in an equation or expression. The other ideas—graphing to find where functions intersect, adding the same number to both sides, or factoring and setting each factor to zero—are different methods or properties used for manipulating equations, not the act of substituting an equal value for a variable.

The substitution property of equality is the rule that you can replace a variable or expression with another expression that is equal to it in any equation or expression, and the value stays the same. This is what you use when you know a variable equals a certain number and you want to simplify or solve by plugging that number in. For example, if x equals 5, then in any equation you can substitute 5 for x. In a simple equation like 2x + 7 = 17, substituting x = 5 gives 2(5) + 7 = 17, which checks out as 17 = 17. More generally, if two expressions are equal, you can replace one with the other anywhere in an equation or expression. The other ideas—graphing to find where functions intersect, adding the same number to both sides, or factoring and setting each factor to zero—are different methods or properties used for manipulating equations, not the act of substituting an equal value for a variable.