If X + 2Y = 2X + Y, then X^2 / Y^2 is equal to

Rearrange the given linear equation: X + 2Y = 2X + Y. Subtract X and Y from both sides (per standard operations on equations) to get Y = X, an operation consistent with linear-equation manipulation rules [1]. Thus X and Y are equal for any solution. Therefore X^2/Y^2 = X^2/X^2 = 1 for any nonzero common value; if both are zero the ratio is indeterminate, but among the provided numeric choices the consistent value is 1. The manipulation and solving approach (moving terms and using substitution or simplification) follows textbook techniques for two-variable linear relations.

Sources

1. [1] https://pwg.gsfc.nasa.gov/stargaze/Salgeb1A.htm