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 solutions set.

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For example: Are the following 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.

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Then again, our equation *x *= 1 has just one single solution, and that is 1.

Therefore, our equations *x²* = *x *and *x *= 1 don’t have the same solution set and are, therefore, not equivalent.

This should not be difficult at all.

If we have two equations that both are having the same solution, this is what are “Equivalent Equations.”

Again, an example. How do we know if the equations *x *= 8 and *x *+ 2 = 10 are equivalent? Well, do the simple math.

The number 8 is the only possible number that makes the equation true: *x *+ 2 = 10, and 10 – 2 + 8.

So our number 8 is the only solution. In our equation: *x *= 8. So we can say that: *x *+ 2 = 10 and *x *= 8 have the same solution sets. So they are equivalent.