I'll try to solve your query by way of an example.

X= 2*Y + a + e , here you go Short on X and Long on Y, and the coefficient of Y is 2. Let's say X=100 and Y=49 (i.e. X's and Y's current price) and a=1 and also e=1.

Now you need to execute a trade to make money when e becomes 0.So in order to make money from the trade, you will sell 1 share of X and buy 2 shares of Y. Now where ever the price will move if your coefficients are same i.e 2 and a=1, the moment e becomes 0 you'll make money.

In this pair trade you don't need to put equal money in both X and Y, but whatever quantity of X you sell you have to buy twice quantity of Y.

I'll try to solve your query by way of an example.

$X= 2*Y + a + e$, here you go Short on $X$ and Long on $Y$, and the coefficient of $Y$ is $2$. Let's say $X=100$ and $Y=49$ (i.e. $X$'s and $Y$'s current price) and $a=1$ and also $e=1$.

Now you need to execute a trade to make money when $e$ becomes $0$. So in order to make money from the trade, you will sell 1 share of $X$ and buy 2 shares of $Y$. Now where ever the price will move if your coefficients are same i.e 2 and $a=1$, the moment $e$ becomes 0 you'll make money.

In this pair trade you don't need to put equal money in both $X$ and $Y$, but whatever quantity of $X$ you sell you have to buy twice quantity of $Y$.