Why X and Y are the most popular variables?

Answer 1

The reason for Y is this:

Much of algebra developed when feathers dipped in ink were the most common writing tools. Ball-point pens, and even pencils, were not yet created. The two easiest letters to write were x and y. Mathematicians needed variables they could write quickly without mixing them up. As a result, x and y are still the two most commonly used variables in algebra. Convenience produced the tradition.

X is a different story:

Algebra has its roots in the Middle East where sciences including mathematics and astronomy flourished in the Islamic world in the 700-1450 period. Muhammad al-Khwarizmi (780­850) was one of the major mathematicians of his time and the author of a number of influential books. One of his major books is on arithmetic and another on algebra. In fact, it is his transmuted name 'algorithm' which we now use to refer to the step-by-step procedures for solving a problem. His algebra book is titled "Kitab al-jabr wal-muqabala" which translates to "the book of calculation by completion and reduction." The Arabic word "al-jabr" is the origin of the word "algebra" which describes the process of moving terms from one side of an algebraic equation to the other to find the value of an unknown. Incidentally, another major figure in the field of algebra is the famous Omar Khayyam (1048­1131), a mathematician and poet, who made significant contributions including describing algebraic equations whose general solutions were obtained some 400 years later.

In algebraic equations, one solves equations to obtain the value(s) of one or more unknown(s). The word for "thing" or "object" (presumably unknown thing or object) in Arabic - which was the principal language of sciences during the Islamic civilization - is "shei" which was translated into Green as xei, and shortened to x, and is considered by some to be the reason for using x. It is also noteworthy that "xenos" is the Greek word for unknown, stranger, guest, or foreigner, and that might explain the reasons Europeans used the letter x to denote the "unknown" in algebraic equations.