System of equations

In mathematics, simultaneous equations are a set of equations where variables are shared. A "solution" will satisfy all of the equations simultaneously. For example, the following is a set of equations:

$x^{2}+y^{2}=1\quad x=2y$

This can be solved by substituting the second equation into the first.

$\Rightarrow 4y^{2}+y^{2}=1$

$y=\pm {\sqrt {1 \over 5}}$

$x=\pm 2{\sqrt {1 \over 5}}$

Often there are infinitely many solutions if there are less equations variables, and no solutions if there are more. Therefore often systems are considered where the number is the same.