Solving for $x$ given $y = 2x - 9$ and $y = 5$. When does the 5 come into play? I am doing some problems. It states "Isolate the left side for each of the following equations. Then solve for x, assuming the value of y is 5 in a all cases." I noticed that I can get two different answers, depending on when I decide to plug in the value of y. For example, this is what I get:
$$ y = 2x - 9 $$
$$ 9 + y = 2x -9 +9 $$
$$ 9 + y = 2x \frac{1}{2} $$
$$ \frac{1}{2} * 9 + y = x $$
$$ x = \frac{1}{2} * 9 + 5 $$
$$ x = \frac{9}{2} + 5 $$
$$ x = \frac{19}{2} $$
But, if 5 is plugged into y in the beginning, I've seen it done like this:
$$ 5 = 2x - 9 $$
$$ 5 + 9 = (2x - 9) + 9 $$
$$ 14 = 2x -9 + 9 $$
$$ 14 * \frac{1}{2} = 2x * \frac{1}{2} $$
$$ x = 7 $$
Which one is correct?

You have a mistake in the first. The second has no mistake. 
For the first, note that
$$\begin{align}9+y=2x&\iff \frac{1}{2}\left(9+y\right)=\frac 12\times 2x\\&\iff \frac{9+5}{2}=x\\&\iff x=7.\end{align}$$
Note that you need to multiply $9+y$ by $\frac 12$.
