Number of ways to algebric expression Suppose I have equations:
x + 2 = 3
y + 4 = 6

Here, x = 1 and y = 2
However, I accidentally discovered that I can do something like this:
Divide equation 1 by 2:
(x + 2)/(y + 4) = 1/2
2x + 4 = y + 4
y = 2x

Now if we substitute the value of x or y in equation y = 2x we can get the value of x or y.
So, what I did is reduced the two equations into one y = 2x.
What is this diving rule called? What is the logic behind this?
 A: Think in terms of constraints :
Firstly, we imagine two real variables such that $x, y$ satisfies the set of constraints $x + 2 = 3$ and $y + 4 = 6$.
Secondly, we define another set of constraints on $x$ and $y$ : they must satisfy $\frac{x+2}{y + 4} = \frac{1}{2}$. It just so happens that the solution to the first set of constraints, $(x, y) = (1, 2)$, also satisfies the second set of constraints. In fact, we can see that it should do so, because this second set of constraints was constructed from the solutions of the first set of constraints.
In other words, what you have done is basically created another set of constraints from the solutions to your initial set of constraints. Obviously, the solutions to your first set of constraints will definitely satisfy this constructed set of constraints.
You can easily create many other sets of constraints which the solution to the first set of constraints will always satisfy (e.g. $x + y = 3$). But if you were to remove the first set of constraints, then the set of solutions satisfying the all remaining sets of constraints might differ.
