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.