# Question about solving systems of equations

Is their a universal method to solve systems of equation, eg do methods such as 'elimination' work for ALL types of simultaneous equations (I am specifically referring to 2 and 3 equation simultaneous equations).

If their is not, why?

I am referring to highschool level equations, to likes of this:

• Yes there is. It is called Gaussian elimination and it involves matrices. See: en.wikipedia.org/wiki/Gaussian_elimination. Also linear algebra is the part of math, which deals with these kind of questions. – 05storm26 May 31 '14 at 8:30
• @05storm26 that is beautiful, i wonder if it would be easy to learn. thanks – mahat May 31 '14 at 8:31
• @05storm26 I don't think gaussian elimination would deal with the $xy=4$ equation, but it will work with the linear equations – Ellya May 31 '14 at 8:39

But one of the equations you gave, the one that says $xy=4$, is not linear. As soon as you start allowing non-linear equations, big troubles arise. If you have even a single equation that contains terms like $x^5$ or higher powers, then it is known that there can not be any simple formula for the solutions. These sorts of equations are called "quintic"; see here for more information. Similarly, equations like $\sin x = x$ can't be solved by any sort of formula. And, naturally, things get even worse if you have several equations in several variables.