Where did the 3 come from though like why multiply by 3?

That technique is trying to eliminate one of the variables. So, the first equation has -3y. The second equation has y. If you multiply the second equation by 3, you have a -3y in the first equation and a +3y in the modified second equation, so now when you add them, you have 0y (this gives an equation only in x).

Another method: In the second equation, solve for y in terms of x (I choose the second equation because the coefficient of y is 1):

$y = 13-2x$

Now, plug that into the first equation:

$4x-3(13-2x)=-19$

After multiplying out, you can solve for $x$ since it is an equation in one variable. Once you know x, plug it into the formula you just created for y.