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 *x² *= *x *equivalent?

The solution: If we inspect this, the equation *x²* = *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 *x²* = *x *and *x *= 1 do not have the same solution sets and are not equivalent.

Next Lesson: Operations that Produce Equivalent Equations

*Last Updated on April 12, 2021.*