Originally Posted by Pmb Even after I read this a few times I still can't see how you got it wrong. The terminology was made clear by the examples.
Is this is serious question or a complaint that I didn't explain it well? 
I didn't get it wrong.
But I did take issue with your use of the word 'insert'
I note you later used the correct term substitution (the corresponding verb is of course 'to substutitute')
There is a world of difference between 'to insert and 'to substitute'.
When you insert you do not change anything that was already there, but you do add something that was not.
When you substitute you replace something(s) that was/were already there.
Failure to make this distinction leads to contorted thinking for example you surely can't be seriously claiming that asking for the solution to the equation x = 3 is meaningless?
Said algebriac equation has but one solution, which is perfectly clear.
As a matter of interest, the OP asked
In the context of simple algebriac equations

Which is why I asked if he understood differential equations.
Not all Maxwell's equations are DEs.
Can you say the same for Einstein's Field Equations?