Editing Elementary algebra (section)

==== Undetermined systems ====

There are also systems which have infinitely many solutions, in contrast to a system with a unique solution (meaning, a unique pair of values for {{mvar|x}} and {{mvar|y}}) For example:

: <math>\begin{cases}\begin{align}4x + 2y & = 12 \\
-2x - y & = -6 \end{align}\end{cases}</math>

Isolating {{mvar|y}} in the second equation:

: <math>y = -2x + 6 </math>

And using this value in the first equation in the system:

: <math>\begin{align}4x + 2(-2x + 6) = 12 \\
4x - 4x + 12 = 12 \\
12 = 12 \end{align}</math>

The equality is true, but it does not provide a value for {{mvar|x}}. Indeed, one can easily verify (by just filling in some values of {{mvar|x}}) that for any {{mvar|x}} there is a solution as long as <math>y = -2x + 6</math>. There is an infinite number of solutions for this system.