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

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

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