Balance
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An equation is equivalent to another equation, if they have the same solution.
If the two equations are linear transformations of one another they have the same solution.
A linear equation in one variable has one solution. An equation of another kind may have none, one, or more - including infinitely many - solutions.
Another solution for x+y = 7 is y = -x+7
In algebraic terms, the solution is the answer to equation.