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.
Next Lesson: Operations that Produce Equivalent Equations
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The transcript of the video is for your convenience. 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.
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