Curves simplify to lines?

Question

I have what is supposed to be a curve:

$$25x^2 - 4y^2 = 100$$

When simplify this to be:

$$y = 2.5x - 5$$

it is a line.

But isn't it supposed to be the same?

Answer 1

It looks like you've gone from

$$25x^2-4y^2 = 100$$

to

$$5x-2y=10\;?$$

This is not a valid operation; the square root (or any other power) of a sum is not the sum of the square roots (or powers) of the individual terms.