Lucia tried to solve the system below. what error did she make?

Lucia made a mistake when she rewrote the formula


To rewrite the formula to x is a function of y. we have to add 2y to both sides of the formula. Instead of adding 2y, Lucia subtracted 2y from the right side.

Instead of what she did, x should be written the following way

The original system is much more of a candidate for linear combination rather than the substitution method which was what was attempted.. Having said that, the mistake I see appears in the very first step of the process when Lucy tries to solve the equation x - 2y = -2 for 'x' in terms of 'y'. Here result should have been x = 2y - 2 or x = -2 + 2y