Editing Elementary algebra (section)

==== Over- and underdetermined systems ====

Systems with more variables than the number of linear equations are called [[underdetermined system|underdetermined]]. Such a system, if it has any solutions, does not have a unique one but rather an infinitude of them. An example of such a system is

: <math>\begin{cases}\begin{align}x + 2y & = 10\\
y - z  & = 2 .\end{align}\end{cases}</math>

When trying to solve it, one is led to express some variables as functions of the other ones if any solutions exist, but cannot express ''all'' solutions [[Number|numerically]] because there are an infinite number of them if there are any.

A system with a higher number of equations than variables is called [[overdetermined system|overdetermined]]. If an overdetermined system has any solutions, necessarily some equations are [[linear combination]]s of the others.