# Equivalent Equations

Let’s begin with the definition of equivalent equations.

We speak of “Equivalent Equations” when we have two (2) equations that are having the same solution set.

For example: Are the equations x = 7 and x + 2 = 9 equivalent? The solution: Our number 7 is the single possible solution of the equation x + 2 = 9.

Similarly, the number 7 is the only solution to this equation: x = 7. Therefore we can say that x = 7 and x + 2 = 9 have identical solution sets, so they are equivalent.

Another example: Are the equations x = 1 and = x equivalent?

The solution: If we inspect this, the equation  = x has two solutions, 0 and 1.

On the other hand, our equation x = 1 has just a single solution, namely 1.

Hence, the equations  = x and x = 1 do not have the same solution sets and are not equivalent.

1. Are the equations $$x = 4 \: and\: x + 8 = 3$$ equivalent?
A.
B.

Question 1 of 2

2. Are the equations $$x = 64\: and\: x - 34 = 30$$ equivalent?
A.
B.

Question 2 of 2

Next Lesson: Operations that Produce Equivalent Equations

Last Updated on April 12, 2021.