# Algebra/Solutions of systems of linear equations

### Solutions of systems of linear equations

A solution of a system of linear equations is a set of numbers for each variable that makes every equation true.

## Number of solutions for a system of linear equations

A system can either have

1. Zero solutions
2. One solution
3. Infinitely many solutions

This can be demonstrated using 2 variable sets of equations.

No solutions

${\displaystyle {\begin{matrix}3x+2y=6\\3x+2y=12\end{matrix}}}$

One solution

${\displaystyle {\begin{matrix}x-y=1\\3x+y=9\end{matrix}}}$

Infinite solutions

${\displaystyle {\begin{matrix}x-y=0\\5x-5y=0\end{matrix}}}$