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?
It looks like you've gone from
$$25x^2-4y^2 = 100$$
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.