What type of equation is this called? I'm trying to solve it. Whatever it is, it's been out of my (very basic) understanding level thus far.  Hahaha I have sheets and sheets of paper trying to work it out. I dunno if it helps, but it's an optimization problem, I'm trying to work out for a piece of software I'm writing. The 'original' equation looks like this...
$\frac{2y}{2 + x} = n$
And I want to see if I'm able to feed in any particular number to N, and solve for the x and y. Like this...
$\frac{2y}{2 + x} = 4148$
At first I tried solving for X and Y like this.(I don't know how to show the steps, so I'm just going to show the 'results'.
$y = 2074 + 1037x$
$x = \frac{8296}{y -1}$
Then I thought I could replace one side with the other.
$x = \frac{8296}{2073 + 1037x}$
But I think that led down the road to madness. And I came here straight away. I think I'm okay. But could someone perhaps shine a bit of light upon my situation?
What I mean by this...is I keep getting different answers, which makes me think I'm really doing it wrong. Also, and maybe this doesn't matter, but x and y are a constant product formula themselves. So, x * y will always equal k(the invariant). I super appreciate any thoughts! Thanks =)
 A: It's unclear (to me at least) how you got from ${2y\over2+x}=4148$ to either $y=2074+1037x$ or $x={8296\over y-1}$, neither of which is correct, but here are simple algebraic steps that lead to correct equations:
$${2y\over2+x}=4148\implies{y\over2+x}=2074\implies y=2074(2+x)\implies y=4148+2074x$$
and
$${2y\over2+x}=4148\implies{y\over2+x}=2074\implies{2+x\over y}={1\over2074}\implies2+x={y\over2074}\\\implies x={y\over2074}-2$$
If you like, the equation for $x$ in terms of $y$ can be written as $x={y-4148\over2074}$.
Finally, in answer to the question in the title, because ${2y\over2+x}=n$ implies $y={n\over2}x+n$, it is, in essence, a disguised version of a linear equation. The name derives from the fact that the solution set, plotted in the $xy$-plane, consists of points on a line. (Technically the point $(-2,0)$ is not in the solution set since $2y/(2+x)$ is not defined when $2+x=0$. This is reflected in the use the implication symbol $\implies$, rather than the if-and-only-if symbol $\iff$.)
A: There are many $(x,y)$ pairs that will solve your equation:

*

*$x=0, y=4148$

*$x=1, y=6222$

*$x=2, y=8296$
In fact, there is a matching $y$ for any real number $x$ as long as $x \ne  -2$.
