What algebraic property is illustrated by the statement “if x = 3 and 3 = y, then x = y”?

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The statement “if x = 3 and 3 = y, then x = y” illustrates the algebraic property known as the transitive property of equality.

The transitive property states that if one quantity is equal to a second quantity, and that second quantity is equal to a third quantity, then the first quantity is also equal to the third quantity. In this case, we have:

  • x = 3 (the first equality)
  • 3 = y (the second equality)

Since both of these equations establish the equality of the number 3 with the variables x and y, we can conclude that:

  • x = y

This property is essential in algebra and mathematics in general, as it allows us to manipulate equations and make logical deductions based on known relationships.

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