When doing data sufficiency, it is best to start by asking ourselves: What do I need? In this case, we need a single equation that will give me one value for x. Alternatively, we could have a system of equations that would give us a single value of x.

Statement 1: This doesn't give us a single value for x. All we know from this is that x is not negative.
Statement 2: This doesn't give us a single value for x. All we know is that x is 4y.
Combined: It may be tempting to say:
y^2 = 4y so let's divide both sides by y to determine that x = 4. However, y could also be 0, and division by 0 isn't permitted. Although linear equations produce a single solution, squares generally produce 2.

To find the answers we could set the equation to equal:

y^2-4y=0
y(y-4)=0

So either y=0 or y=4.

(E) is the best answer. If we cannot come up with a single value for y, we will never be able to come up with a single value for x.