They are simultaneous equations
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Equivalent equations are equations that have the same solution set.
There is no special name. Two totally unrelated equations could have the same solution(s).
Equivalent Equations
Coincidental equations are really the same and are the same line. They have infinite solutions meaning that any solution for one will be a solution for the other.
It is a set of equations, which is also called a system of equations. There may be no solution, a single (unique) solution or more than one - including infinitely many.